Exponents and Powers Overview

Hello kids, how are you? I am Sakshi Kishorewal, your mathematics mentor, your teacher, your guide. So today we have brought a new chapter on your demand, which is Exponents and Power. Now we will understand Exponents and Power very easily. And if you understand this concept well, then 8th standard is like this. I repeat that this statement is said in every lecture. Yes, I tell you every lecture because this 6th, 7th, 8th are so basic building blocks of your life that wherever you get hold of it, things start to run very smoothly. That's why I say this thing. So, we will start today's chapter, Exponents and Powers. So, to start this, what does ma'am say first? Copy or paper or pen. ready rakhna hai ma'am aaj bohot saare questions karayenge jaisa har baar karati hai to aaj hum log jitte bhi questions karege wo saare questions ko aapko kya karna hai apni copy mein ma'am ke saath solve karna hai aur aapko apne aapko ratings dena hai aur kya likta hai jaisa aap chat box mein likte ho ma'am i am a 7 star i am a 4 star i am a 5 star i am a 6 star kid write that in a chat box so let's begin with today's class that is what Topic to be covered. What are we going to cover today? Exponents and powers, laws of exponents and expressing the large number in the standard form. To be very honest, to be very honest, kids, that all these topics, this topic, this topic and this topic, we will teach you in 7th, we will teach you in 8th and we will teach you in 9th. But its forms change little by little but basics never change. On basics, once you get a command, you are like, oh. I can do this right so this is the way of doing so First thing tell me one thing that what is the need of exponents and powers I will tell you all the other things that what is the same of exponents and powers We will tell that too First thing why is the need of exponents Now I said do you know the mass of the earth is like 590000 kgs Can you read this number are you able to read this or not Or I say that mass of Uranus is this Now tell me which is greater mass? So what will you do? Count the digits. We know how to count the digits. But not counting the digits. Assume that this has equal number of digits. Equal and equal number of digits. So first of all you are able to read it. First of all to read it you have to 5, 7, 5, 9, 7, 0, 3 times 0, 4 times 0, then this this this this this, 0. This is the way you say it. Now you will say that we will add other things like million, trillion and so on. But it doesn't sound good, right? It seems to be really cumbersome stuff. So what we will do is we will learn a new format to write these big numbers in the exponents form. So today's class is on the topic of if you ever get big numbers in your life, then what can we do with big numbers? we can write it in shorter form and it is much much easier to compare it now you know that Uranus is very big to earth now you will say that you taught me geography I know that Uranus will have more mass to the earth comparison but now I tell them to read it so is it easy to read? do you find it easy to read the mass of the earth and the mass of Uranus? simply no ma'am So, this is how our... what happened? Introduction of this chapter happened that is what? Exponents and powers. Now which field is this exponents and powers? Let's see what is this field? Right, so what is exponents? Whatever is the large number, we write this in the shorter form. For example, I have written 8 cube, what do we read this? 8 to the power 3. Now what is the meaning What does 8 to the power 3 mean? Look, whenever we... multiplied by 3 times. So, what we multiplied? 8. The one we multiply by 3 times, we call it base. How many times we multiplied? 3 times. The number of times we multiply, we write it up here. That is known as what? Exponent. So, basically, if I tell you that 2 x 2 x 2 x 2 x 2. Abba Tov! How many times is 2 multiplied? 1,2,3,4,5 So what will be the base? Who are we multiplying? 2 So we are multiplying 2 This is your base or not? How many times are we multiplying? 5 times So this is your exponent Yes or no? The one we are multiplying, the one we are multiplying That will be the base And how many times are we multiplying? That is the exponent Is this concept clear or not? Now how do we read this ma'am? We read this that is base to the power. We read this that is 8 is the base, 3 is the exponent and 8 cube is the exponential form of the 5 to the power that is form of 512, right? So, now let's read it or we read 8 cube or 8 raised to the power, what we read? We read 3. How much power we have applied on 8? 3 powers, right? That is known as what? 8 raised to the power 3 or we say that 8 cube, right? When we have ever, now listen to me one more thing. Let's see here. This can be read as what? 8 raised to the power of what? Beta 3. Now, ma'am, you will think that, ma'am, here, let's assume you have 6 cubes written. Now, what is 6? Come on, come on. What is 6? This is the base number. What is 3? It is your exponent. And here, look, here it is written, the big number. The number multiplied. How many times have we multiplied this? That is what? Beta, we say this is known as best. Now, let's assume, if it is written in front of you, 12 into 12. Now what will be written here? Will we write 12 to the power 2 or not? Or 12 raised to the power 2? Now what is 12? 12 is bigger But who will we multiply? This will be your base and 2 will be your exponent Now, Is exponent and power the same? No, there is a slight difference in this What is the slight difference? What is exponent? How many times did you multiply 6? you that is what beta teen bar that is your exponent but you poor a joke Tom hey yeah Joe poor a term with a high AC both a half power the power key definition kia Houthi a the base and the exponent together matlab base or exponent ko job poor a little a that is known as what beta power so agar up case I'm a cubby as a little yellow house six to the power to yellow house six or yellow house six to the power for my book cheese sick of you Whenever you write power 2, then the way to read power 2 is called 6 square. That is we say this is a 6 square. Here 6 raised to the power 2 is not called. We are specific in 2 and 3 because 2 is called square and 3 is called cube. And as 4, 5, 6, 7 comes, we put raise there. What will we call this? Here 3 is power, so what will we write here? Its exponent is 3, so what will we write? 6 cube. Now what will you write here? Here its exponent is 4. So we will write 6 raised to the power 4. Suppose you have 6 to the power 10. How much is the exponent in 6? 10. So how do we write this? We write 6 raised to the power 10. So basically we learnt that Exponent has a base and the base of exponents and power The more you multiply it, the more your exponent is And this whole thing is called power We call the whole thing power Now let's do a quick question I said express 256 as the power of 2 So do simple prime factorization which we have been doing since childhood Chalo! Whatever you do with me or whatever you do with me first tell me Factor 256 So what will be the prime factor of 2? 128 Then we will do it with 2, that is 64 Then we will do it with 2, that is 32 Then we will do it with 2, that is 16 Then we will do it with 2, this is going to be 8 Then we will do it with 2, this is going to be 4 Then we will do it with 2, that is 2 And this is 2 and from here how many times? 1 Now how many times can we write 256? How many times? 1,2,3,4,5,6,7,8 times or not? 1,2,3,4,5,6,7,8 times If it was 10,11,12,15 times then how would you feel? Do we have any shorter form? Obviously it has shorter form So tell me, what will be its base? It is 2, so it is 2 Now what will be its exponent? How many times did you multiply? 8 times So 256 can be written as what? 2 to the power 8. Very simple. Very very simple. Right? Now, I will tell you which one is greater. 8 to the power 2 or 8 square and 2 to the power 8. Which one is greater? Tell me a simple thing. Now tell me. What is the meaning of 8 square? What is the meaning of 8 square? Say it fast. Say it fast. Whoever writes before me, Ma'am, my question number 2 is before you. Before you. What is the meaning of 8 square? 8 into 8. That is what? 64. What will we call this? 8 square. We can also say 8 raised to the power 2. but 8 square sounds little good and actually everyone is familiar with it right Now what does 2 power 8 mean? 2 times 2 is 8 times 2 times 2 is 3 this is 4 this is 5 this is 6 this is 7 and this is 8 Now we have just taken 2 power 8 in the previous question That is what? 256 So it is a simple thing It is a simple thing That is 256 is what? Greater than what? 256 is greater than that is what? 64. So 2 to the power of 8 is greater than that what? 8 to the power of 2. Answer. Yes or no? Very easy peasy, lemon squeezy, right or not? Now, coming to next question. Now, expand. Now, it is written expand a cube b square. What did we read? What did I read? Listen to me. a cube into b square, right? Then I wrote a square into b cube. This is written b square into a cube. and it is written as b cube into a square means when power is 3 then what word we will say? cube if power is 2 then what we will say? square so first one expand are they all same? see now tell me one thing before this we have read a chapter what chapter we had read? before this what we had read? that is algebraic expression in algebraic expression we have read like terms what we had read in like terms? we had read like terms that We will write the factors of all the numbers In factors, we will see that all the variables We did not talk about numerical factors We only talked about variable factors If the variable factors are same If it has 2x and 2x It has y and y Then these will be like terms Yes or no So we have to do the same If you look at this question carefully, then what is written here? a cube b, b square, means a is 3 times and b is 2 times. So, look at this, a is 3 times and b is 2 times. So, is a 3 times and b is 2 times in this also? So, these two will be same. Then look at this, a square b cube, means a 2 times and b 3 times. So, in this also, say a 2 times and b 3 times, is it not? So, these two will be same. You did it here only. You did the question here only. For this you don't have to do this also. Expand this, do this, do that. But we will do it. We have asked the question, we will solve it. So what is said? Come on, let's solve it quickly. So what is the meaning of a cube b square? Like we did in the last class. a into a into a into b into b. Right? Then what is written? a square b cube. So how much will this be? a into Right? Then what is written? b square a cube. So how much will this be? b into b into a into a into a. Yes or no? Then what is written? b cube a square. So what is written? b into b into b into a into a. So which one is same? This one is same. Right or not? So can we say that a cube b square and b square a cube are same? Yes or no? And which one is same? This one and this one. That is a square b cube. And b cube a square are what? Same or not? Simply same. Yes. Shoo shoo. Kataam. Yes or no? Very very easy. Chalo. Express the following number as the product of its prime factor. Dekho bhai, main tumhe jaan bhoot ki bohot saare questions karaati hu. That's why my video go little longer. Main chahun toh aapko bohot kam questions kara sakte hu. Toh jabab questions... questions then only you will able to practice. So till now all the questions that you have done are you doing in copy making or not? If you are doing then write in the chat box ma'am I am solving with you. Some children write ma'am I do the questions along with you in the chat box that is really heart touching that yes you children are studying with us. Right so what is written as the factor of prime factor. So before me who will write 72? Write that I did the prime factor of 72 before you. If we do prime factor of 72, then it will be 36, 18, 9, 3, and 1. So how can we write 72? We can write 72 as 2x2x2x3x3. So how many times 2 came? 3 times. And how many times 3 came? 2 times. So we can write 72 as 2 cube and 3 square. When needed. Second question, factor 432. So, before me, who will do it? Write it in chat box that I did it before you. So, let's do a race. Let's do a race. So, how much is 432? So, we have done prime factor. So, how much is 2? 216. Then, how much is 2? 108. Then, this will be 2. This is what? 54. 2. That is what? 27. Then, this is 3. 3 to 9, then 3, then 3 and then 1. Right or not? So what can we write 432? 432 can be written as what? How many times? 1, 2, 3 and 4. How many times? 1, 2 and 3 times. So this can be written as what? 2 to the power of 4 into 3 to the power of 3. That's it. Very easy peasy or not, right? Now coming to your next question. Exponents of negative number, listen very carefully. Listen very carefully. Look, I had taught you this in integers. If you have seen my video in integers, then I had taught you this there too. But I had told you one thing there, that if negative is more... times multiply karte to answer ki aata beta or data mother negative at a or negative number ko agar may even times multiply karte you to answer ki aata beta positive may at a to see in thing applies over here with the exponent job many bola to marry bar snow German integers may pariah kha many lakota minus 1 into minus 1 into minus 1 the minus cook it in a bar multiply kare take that is what negative was multiplied by what odd times or not yes on times means we didn't read exponents there. So now can we write it like this? 1 to the power 3? Yes or no? Did I teach this thing 1 minus 1 multiplied by odd times and even times or not? So when we said odd times there, can I call it power 1 by 3? And how will the answer be? Will there be a negative answer or not? Remember, the same thing which I taught you in integers, The way of speaking is different. If I write minus 2 into minus 2 into minus 2 into minus 2. So, what I had studied in integers. What is happening here? Minus 2 is multiplied 4 times. Is it even times or not? Or I can write it like this. Minus 2 power 4 or not. Yes or no. So, the power of negative. If it was even times, then remember. Negative multiplied by even times give you answer as what? Positive or not. Remember, this ma'am has taught you or not. This ma'am has already taught you. Then after that, today I am just telling you a method that we can think of it this way. So this means that, this means that, whenever you have, like suppose I gave you a question, minus 2 multiplied by minus 3 multiplied by minus 3 multiplied by, 2. Let me give you a question. Remember, what did we learn? 1 times negative, 2 times negative, 3 times negative. Yes, isn't it? If 3 times negative comes, remember, how did we learn? We learned like this. Look, we had said earlier that 3 times negative. So, if negative is 3 times, then the answer will be negative. Then what did we multiply? 2 x 3 x 3 x 2. So, 3 x 3 is 9, 9 x 2 is 18, and 18 x 2 is what? Minus 36. Will its answer come or not? Remember it with simple integers This chapter is a very good chapter If you have command on integers then first And if you know algebraic expressions then this chapter is also like this It is easy to understand So this means If ma'am writes in front of you Minus 2 to the power 57 So will its answer be negative or positive Its answer will be 100% negative Because the power of negative is odd. Yes or no? So we saw that if the power of negative is odd. Or if I say that I have multiplied negative by odd times. Yes or no? So the answer to this is negative. And if I say that the power of negative is even. Or if I say that I have multiplied negative by odd times. So the answer to this is positive or not? Simple thing. So, how will be the power of minus 2, 57? Will there be a negative answer or a positive answer? It will be negative. We just asked whether it will be negative or positive. Now, I asked, what will be the answer of minus 3, 104? Will there be a positive or a negative answer? So, how will the answer be? It will always be positive. It will always be positive. So, keep this in your mind that some points to remember means, If the power of negative is odd number, then it will always give negative answer. If the power of negative is even number, then it will always give positive answer. Now, if I write a cube b square, then it is equal to a square b cube. Remember like terms. Are these like terms? No, they are not like terms. Then I said that a square b cube is equal to b cube a square. So, what is this? Is it a light term or not? This is like term, this is like term, this is like term. So, that's why this chapter is put so low in your NCRT book. Because you are expected to know integers. Till when you will know algebraic expression When you will read all these things properly Then you will understand what will happen It is a game of little things Let's move on to the next thing Workout So what is written here Workout 1 to the power 5 Minus 1 to the power 4 Minus 1 to the power 5 So what is written here 1 to the power 5 Someone's power is positive power 5 three, four. and this 5 will be 1 minus 1 to the power 3 now minus is minus to the power odd so minus to the power odd will be negative 1 or not simple now I said minus 1 to the power 4 so negative to the power even will be plus 1 simple plus 1 what is written minus 10 to the power 3 now see first thing what is written minus 10 to the power 3 if you open this open this So what is written? Minus 10 into minus 10 into minus 10 is written. So minus is 3 times, so the answer is minus. And how many times is 10? 3 times, so 1000 is given. Here I will tell you in short. So first thing is minus 10 to the power 3. So its answer will be 100% minus. Negative to the power 3 is what? Negative to the power odd is negative. Now how much is 10 to the power 3? So we have to multiply 10 3 times. It is very easy to multiply 10 3 times. So minus 1000 is your answer. Now what is written? Minus 5 to the power of 4 Now see what is written? Minus 4 into minus 5 into minus 5 into of minus 5 Right or not? Now tell me one thing How many times is negative? 1,2,3,4 So the answer will be positive Now 25 into 25 How much will it be? 625 or not? Or we could have written it like this Negative to the power of even is positive And 5 to the power of 4 is 5 into multiply it and it will be 625 is your answer so without opening it you could have answered the question now coming to laws of exponent listening very carefully is very easy first thing is that do you have base clear when I am starting laws of exponent before that you write in chat box before I starting my laws of exponent you write that ma'am before laws of exponent I have clear base I have clear exponents and power When I have clear like and unlike terms When you write this much in the chart box Then you will understand it very quickly So first look Laws of exponent of the what This is called addition If you have I tell you 2x2x2 What is written here? 2 cube is written Yes or no? Ok I write 2 to the power of 4 So what is written here? 2 x 2 x 2 x 2 x 2 Right? Now I will tell you What is 2 to the power of 6? See, this will be 2 x 2 x 2 x 2 x 2 Ok, I will write it like this Let me explain it to you Listen to me first Then you will understand what is written above Now see I am multiplying these two So what will be this? 2 to the power 2 into 2 to the power 4 How many times is this? Multiply 2 to the power 2 2 to the power 3 This is 3 Into 3 And into 2 into 2 into 2 into 2 into 2 Right? Now tell me How many times did 2 come? 1, 2, 3, 4, 5, 6, 7 Did 2 come 7 times or not? This is equal to what? 2 to the power 7 And here what was written? 2 to the power 3 into 2 to the power 4 So now here you see Is your base same? And what is the base in multiplication? What is the base in multiplication? So here, what is the power of 2? 2 to the power of 7. So could we have written 2 to the power of 7 as 3 plus 4? Yes or no? So this means that if ever in front of you the base is same, if we multiply the powers which have the same base, then we add the exponents. What does it mean? That if in front of you, 2 power 3 and 2 power 4 are multiplying What is the base of both? Is the base same or not? If the base is same, then both the exponents are simply added And we have learnt this logic just now So this is its general form If there is a power m multiplied by a power n Then what happens in this? The exponents of both are simply added If I give you an example Tell me quickly 8 to the power 3 plus 8 to the power 4 is how much? Say it quickly. 8 to the power 3 plus 8 to the power 4 is how much? Say it before me. How much is 8 to the power 3 plus 4 which is equal to what? 8 to the power 7. Simple. Very simple. Now it comes that when you both I wrote 2 to the power of 4. Have you seen this? 2 into 2 into 2 into 2. Now what I am doing is, I wrote 2 to the power of 3. So this will be 2 into 2 into 2 into 2. Right? I am doing 2 to the power of 4 divided by 2 to the power of 3. So this will be 2 into 2 into 2 into 2. And what is written here? 2 into 2 into 2. So this 2, this 2 cancel, this 2, this 2 cancel, this 2 and this 2 cancel. So what is the answer? 2 to the power 4 divided by 2 to the power 3 is equal to what? 2 to the power 3. Now if 2 is written, can I write it as simple power 1 or not? Can I write it as 2 to the power 4 minus of 3 or not? If 1 is required, can I write it as 4 minus 3? So if you have two exponents or two powers and both have a base... same and both are in division then powers simply subtract. So if we divide the powers which have, both have powers, we are dividing and if their base is same then subtract the exponent. Pick up the exponent and subtract. So I said that is its base same, its base same. Its power, its exponent is different. So what we will do is subtract these two exponents. Now here it is said that the exponent of your numerator is greater than your denominator. Right, say an example. If I say 8 to the power 4 divided by 8 to the power 3, then how much will it be? Say it quickly. Can I write this as 8 to the power 4 minus 3 which is equal to what? 8 to the power 1 which is equal to 8. Yes or no? Look at the third law. Third, quickly write it with me too. What is written? If we have to take the power of the power then we have to multiply the exponents. So now see, I wrote, I am changing the color, right? I wrote 2 to the power 3, right? 2 to the power 3 to the power 2, yes or no? I wrote this. So what does this mean? This is the base inside, this is the whole base. So what is written here? 2 to the power 3 into 2 to the power 3, written twice or not? Yes or no? You tell me one thing, if I hide it like this, then will this whole 2 to the power 3 be the base or not? If 2 power 3 is the base then what is written here? We have opened it twice Now see here its base is same and here its base is same So what will be the powers? 2 power 3 plus 3 which is equal to what? 2 power 6 Now if it is required What is required? I could have written 2 power 3 into 2 or not So what will be 2 power 3 whole to the power 2? Simply multiply both of them If I ask you a question Here, we are opening the answer of a to the power of m So the answer to this will be by multiplying both of them So if I tell you that 8 to the power of 3 into 4 So what is written here? This is your base, so how many times will you open the base? 8 to the power of 3, will you open it 4 times or not? 8 to the power of 3 into 8 to the power of 3 Yes or no? Now, the base of all is the same What is the multiplication of 3 and 4? powers will be added so 8 power 3 plus 3 plus 3 plus 3 what will happen? so how much will it be? 8 power 12 or not? which is equal to what? 8 power 3 into 4 or not? simply yes or no? so what to do? if these two are on the base and 2 powers are on the multiply then what to do with simple powers? multiply them what to do? multiply powers so this is your what? third law now coming to your fourth law what does the fourth law say is that How to multiply the powers with the same exponent? If we have to multiply the power where the base is different, but base is different. Base where the base is different, but the exponents are same, then we multiply the base. What is he saying? Look, he is saying that when the base is different, and power is same. Like I said, 2 power 3 and 4 power 3. Yes or no? Is its base same? Sorry, its base is different. I will subtract 4 power 3 and make it a little bit 5 power 3. It will be easier. You will understand better. So, its base is same, different and its base is different. But will both the exponents be same or not? Yes or no? So, what is written here? I can write this as 2 into 2 into 2. And what can I write 5 as? 5 into 5 into 5. Now, what am I doing? I am doing pairing. So, I will pair this and this. There is no difference in multiplying. So I wrote 2x5 as one pair and then 2x5 as a separate pair. Right? And could I make this and this as a separate pair or not? So what is 2x5? It is simply 10. Then what is 2x5? 10. And what is this? 10. So what is this? 10 to the power 3. Yes or no? So when needed, is 2x5 to the power 3 written or not? So basically if your base is different and exponent is same then what happens? Power becomes separate and also becomes together So what is written here? A power m into B power n So what will happen? Both of these multiplied and what will happen? This will be m Base is same so what will happen? M will happen For example I wrote 8 power 3 So its base is same, its base is different, not base same, base different, base different, exponent same, exponent same. So what will happen? 8 into 4 to the power of beta 3 which is equal to what? 32 to the power 3. So if you write its opposite, sometimes it is written like this, 2 to the power 3 to the power 5, so what will happen? 5 will climb on this and 5 will climb on this. So what will be written? 2 to the power 5 into 5, sorry 3 to the power. How much power will be 3? It will be 5. Simple. So basically if we save the base different, the exponent same, then what will you do? You will make the exponent a corner, you will multiply both and write it as it is. So this is your fourth law. Now coming to your fifth law. What does the fifth law say is that if you have to divide the power, see it has a lot of laws. If we have to divide the power where the base is different, is different. Base is different but the exponent are same then we divide the base. See what is written here. Listen very carefully. It is very easy. I wrote 2 to the power 3 and what did I write? I wrote 5 to the power 3. Again I said base is different. Now what happened? Both were in multiply. Base was different. Exponent was same but both were in multiply. If they were in multiply then what to do? Multiply base and exponent will be same. Now both of them. What is it? The base is different and the exponent is same. But how are they in division? So what is written here? It is written 2 into 2 into 2. And what is written here? 5 into 5 into 5. So can I write 2 by 5 in one bracket? Can I write 2 by 5 in one bracket? Can I say 2 by 5 or not? So is 2 by 5 whole power 3 when needed? Same thing is applied. That is 2 power 3 and 5 power 3. So when you multiply, So, same thing works and division works the same thing. So, when both are multiplied, multiply it and separate the exponent. And when it is divided, write it like this. So, if I say 8 cube upon 4 cube, then how much will it be? 8 by 4 cube and this and this will be cancelled, how much will it be? 2 cube. Yes, this one. So, if I say 8 cube divided by 4 cube, then first you take out the power of 8, then 4, then you do cancellation. So, how much work does this do? Is it long or not? and this made your calculation much much much much easier right now if you have okay if your exponent is 0 like I said 3 power 0, 4 power 0, 5 power 0, 7 power 0 then what will be the answer listen carefully it is very easy I wrote 2 power 3 divided by 2 power 3 so how much will it be 2 power base same base what did I write 2 into 2 into 2 How much is this? 2 x 2 x 2. So, how much is this cut cut cut cut cut cut cut cut? 1. So, 2 to the power 3 divided by 2 to the power 3, how much is 1? Right? Now, tell me one thing. Am I more? Look more. Son, 2 to the power 3 divided by 2 to the power 3. Base same? Base same. And both are base same and how? In division. So, what will be base? Son, will exponent be subtracted or not? 2 to the power 3 minus of 3 will be or not? Which is equals to what? 2 to the power 0. to So, 2 power 3 by 3, how much is its answer? 1. Once the answer is 2 power 0. So, can we say that 2 power 0 is 1 or not? Yes or no? So, we came to know that anyone's power, anyone's power, 7 power 0, 22 power 0, 1,101 power 0, or I say 1,05,051 power 0, its answer will always be 1. no matter what, its answer will always be 1, right? So, the power of 0 of any one, as we took it out from this, this is its proving. This is how you prove that how to get the power as. The power of 0 of any one is always 1. So, if I say, what is the power of 0 of 8? It is simply 1. Now, I will tell you, any exponent, If I say that the power of any one is exponent 1, then what will be the answer? Will it be the same or not? So what will happen? Any number Any number with the same exponent is equal to the number itself. What will happen? It will be equal to itself. So, a to the power of 1 is equal to what? Simply a. So, what will be the power of 8? Simply 8. Right? Now, let's come to using. Let's do questions. Now, it's your turn. It's your turn. So, in your turn, I will start giving stars from here. I will start. Right? So, from here, do you understand the laws of exponent or not? First thing. If you really want to understand the laws of exponents, then write all the laws in a copy. Write all the laws in a copy. What laws will you write? What laws will you write? I guess I have space here. Look, we know that the power of A is m. I will write it once. What is the power of A? If the base is same and in multiply, powers add. Right? Then we read the second. that if A is the same base and in division then powers get subtracted remember as I am saying third we read that if A is the same power m and if it is multiplied then it becomes A power m into n fourth we read that A power m into A power n base is different a to the power m into b power m. Based different exponent say multiply me. So, what will happen? a into b to the power. How much will be beta m? Then we read fifth. If a power m base same and both are in division and exponent same. So, how much is this? a by b to the power m right. Then we read sixth. Someone's power is 0. Someone's power is 0. How much is beta 1? And someone's power. That is someone's power. I am saying again and again. If someone's exponent is 1, then the answer to that is number itself. So, we have read all these things till now. And these are laws of what? These are laws of exponents which we are going to use in the coming questions. And let's see how quick you are. Okay, use the laws of exponents and simplify and write the form in the exponential form. So, what is the first one? Look, the first one is base, base, base, same. Base, same. So, which laws will we use here? that is a to the power m into a to the power n is equal to what? a to the power m plus n. Right? So, how much will this be? 3 to the power 2 plus 4 plus 8. So, how much will this be? 3 to the power 10 or 14. Will it be or not? Leave your answer in like that. If this is correct, then give 1 star. Right? Coming to your next question. What does the next question say? Here, look. Base is same in both divisions. That is, what will we write here? a to the power m divided by a to the power n. So, what will happen? Exponents will be subtracted. So, what is written here? 16 to the power 15 upon 6 to the power 10. Which is equals to what? 6 to the power 15 minus of 10. Which is equals to what? 6 to the power 5. That's it. This is 2 stars. Quickly. Quickly. Very quickly. Now, coming to your third question. Now, see. First thing is this division. Now, see here. Its base and this base are not the same. Here, 5 to the power 2 is there. And here, it is only 5. So first of all we will simplify this So we know that A power m multiplied by A power m is equal to A power mn So if we simplify this then it will be 5 power that is 2 multiplied by 3 divided by 5 power 3, so this is equal to 5's power this will become what 5 to the power 6 divided by what 5 to the power 3 yes or no? now what is in this? both the bases are same and what are the exponents of both? both are in power and divided so what will be the exponents? that is 5 to the power 6 divided by 5 to the power 3 which is equal to what? 5 to the power 6 minus 3 which is equal to what? 5 to the power 3 now 5 to the power 3 is a very small number which we multiply and tell we have to leave it in exponential form leave it leave it don't tell the answer that is 5 to the power 3 is your answer right? Coming to your fourth part. What will we do in this? Look, what will we do in this? Here, which one of these we will use? That is a to the power m into n which is equal to what? a to the power mn we will use. So, how much is this? 3 to the power 4 into 3. That is 3 to the power 12. What will we do with the first question? We will give here, 2 star was done. Here, 3 star. Right? We will do this question 4 star. Write 4 stars. Now next question. Simplify. Quickly simplify. Now see, when you have to simplify this question, in the question of exponents, open your ears and tie a knot in your mind. Tie a knot in it. Whenever you solve the questions of exponents, always make a common base. What do you make? Make a common base. If you solve this question before me, then give yourself 10 stars. Literally give 10 stars. This is a good question. Now, To simplify this, always make the base same whenever possible. Whenever possible. Now watch. Now we will do prime factor for each one. I am doing it here. What can we write for 12? We can write 12 as 4x3. Yes or no? If we do the factor of 12, what will it be? 2 square x3. Now remember, its power is 3. So here the power of the whole will also be 3. Do you remember or not? Then remember that this power goes to this and this power goes to this. So how much will it be? 2 power 2x3 x3 power 3. which is equal to what? 2 to the power 6 into 3 to the power 3. We have broken 1. Now see, how can I write 9 first? Could I write 3 square or not? How much was the power of 3 there? 3 is there. And how much will be the power of 3 here? 3 will be there. We have applied power on both sides. Now what will happen here? Both will multiply. So how much will it be? 3 to the power 6 will be there. Right? What can we write for 4? We can simply write 4 as 2 square. There is nothing in this. Now see, what can we write for 6? 2 into 3. Right? Now what is written there? That is power 3 and this is also written as power 3. Now if the exponents are same then what will happen? Powers will be distributed. This will go to this and this will go to this. So which is what? 2 to the power 3 into 3 to the power 3. Then what is written? 8. We can write 8 as 2 into 2 into 2. Now do this. That is 2 cube. So what will be 8 square? So here also we have put 8 square. Which is equal to what? These two will multiply. That is 2 into 3 which is equal to what? 2 to the power 6. Now what is written in the last? 27. So what can we write for 27? 3 power 3. Can we write or not? Now you see carefully that I have written all the numbers in the form of a new exponent or not? And what is the base of everyone? 2 or 3 is coming or not? What is the base of everyone? 2 or 3 is coming. So first thing, see how will we solve this? How will we solve? 12. We could write 12. We could write 12 cube. 2 to the power 6 into 3 to the power 3. 9 to the power of 3 is 3 to the power of 6 And 4 to the power of 2 square Did you get it? Now, what could we write for 6 to the power of 3? That is 2 to the power of 3 into 3 to the power of 3 Right? Now, what could we write for 8 square? 2 to the power of 6 And 27 to the power of 3 square Now, what should we do? In numerator and denominator, first do the base same Right? Now, see, is this base and this base same? Yes or no? So if the base is same then what happens? Adds And is this base and this base same? So what will be the powers of these two? Adds So what can I write? 2 to the power of 6 plus 2 into 3 to the power of 3 plus 6 Yes or No? Whole divided by In this, it is 2 and here it is 2 Yes or No? So how much will it be? 2 to the power of 3 plus 6 into 3 to the power of this and this is it or not? So 3 to the power of 3 plus 2 Now how much did it become? 2 to the power of 8 times 3 to the power of 9 whole divided by 2 to the power of 9 times 3 to the power of 5 now what will be the next step? now their base is same and their base is same if base is same and both powers are in division then exponents get subtracted So, how much will be the answer of this? 2 to the power of 8 minus of 9 into 3 to the power of 9 minus of 4. Which is equal to what? 2 to the power of minus 1 into 3 to the power of 4. Leave your answer like this. That's it. Correct. And if you get this answer right. Ya, ya. Many children will write it like this. That is, they will write it like this. I don't have space, I guess. Some children will get the answer. power 4 upon 2 to the power of 9 minus of 8 Means he has reduced this 8 to the power of 9 So now the answer will be 3 to the power of 4 upon 2 to the power of 1 So both the answers are right You can quote any of your answers Yes or no So if this is correct Then please give yourself at least A 5 to 6 star 1, 2, 3, 4, 5, 6 and 7 7 star 2 Now the next question is Simplify Now what word is given here? Simplify Now simplify this, this is comparatively easy Here what we have to do is, as we used to study algebraic expression In algebraic expression we used to multiply number by number So this is the number and this is the number. So what is 2 cube? 2 cube is simply 8. What is written here? A cube. Right? What is written here? 5 and what is written here? Into a to the power 4. Yes or no? Now multiply the number with the number. So if we multiply the number with the number, then what will happen? 8 into 5 is 40. Right? Now what is here? Its base and its same, and what are the exponents? The base of these two is same. So what will be the exponents? Beta beta powers don't have power in multiplying And what will be the exponents? Simply add So into a to the power 3 plus 4 Which is equal to 40a to the power 7 This is your 9 So for this we will give only 5 star 7 star was that question Right? Good to go? Good to go? Good to go? Right? Now one more question Simplify You guys do this question quickly Do it like that Break it Break it by lifting everyone See, 2 is already break, so what can we write? 2 to the power 1. 3 is already break, so what can we write? 3 to the power 4. 2 to the power 5 is already break, that is 2 to the power 5. What can we write for 9? We can write 3 square. And what can we write for 4? 2 to the power 2. And what will be its square? That is 2, which is equal to what? 2 to the power 4. Yes or no? Pick up everything and keep it in this. So, how much will it be? 2 to the power 1 into 3 to the power 4 into 2 to the power 5. divided by 3 square into 2 to the power of 4. Yes or no? Now this and this base are same. So how much is 2 to the power of 1 plus 5 into 3 to the power of 4? Divided by 3 to the power of 2 into what? 2 to the power of 4. So how much is this? 2 to the power of 6 into 3 to the power of 4. Whole divided by 2 to the power of 4 into 3 to the power of 2. Is the power of these two same? Right or not? What are the powers of these two? Sorry, what are the powers of these two base and division? So, the exponents will be subtracted. So, what will be the answer? 2 to the power of 6 minus 4 into 3 to the power of 4 minus 2. Which is equal to what? 2 square into what? 3 square. So, what is 2 square? 4. And what is 3 square? 18. So, what is 18 to the power of 4? 36. 72 is your answer. For this, 6 star. 4, 5 and this 4. Right. Now, say. true or false and justify your answer. Quickly, what will be 10 into 10 to the power 11? 100 to the power 11, true or false? Quickly say it. If we simplify this, base same, then what will be the powers? How much is this? Power 1. So 10 to the power 1 plus 11 will be what? 10 to the power 12. So can this ever happen? No, it can't. Simply false. Simply what happened? False. Right? Now coming to your next question. It says that 2 cube is greater than that of 25. So how much is 2 cube? 8. And how much is this? so this is what? false now third says 2 to the power 3 into 3 to the power 2 is what? 6 to the power 5, this is wrong, neither the exponent is same nor the base is same so multiply this and see, so 2 to the power 3 is what? that is 8, 2 to the power 3 and this will be how much? 3 to the power of 2 is 9 so 9 into 2 is how much? 8 into 9 is 72 now 6 into 6 into 6 into 6 into 6 5 times so 6 into 6 is 36 36 into 6 is how much? this value is 216 so this value will never be equal then after this 216 into 6 into 6 so this value is very big so this also will be false simply false coming to the next part 3 to the power 0 and 1000 to the power 0. So, what is the value of any power 0? How much will this be? It will be 1. How much will this be? It will be 1. Any power 0 is what? 1. So, this is what? 2. Simply 2. Right? Now, till now, as we had talked in the starting, that the mass of the earth and the mass of the Uranus was a very, very, very, very large number. So, ma'am, till now, you were teaching these laws of exponents. We are going to talk about that only If you have any number written For example this number We are writing it as 247,983 So we write 2 x 1 lakh 2 x 4 x 10,000 7 x 1000 Now one more thing Can I write 10 to the power of 5 or not? Can I write 10 to the power of 4 or not? How do we write 100? 100 can be written as what? 10 into 10 which is equal to 10 to the power 2. 1000 can be written as what? 10 into 10 into 10 which is equal to what? 10 to the power 3. So if I say I want to write 10,000, then how many times do we multiply 10? 10 into 10 or into 10. So 4 times 0, how much will it be? 10 to the power 4 or not? So could we write any number in 10 to the power or not? Now look at the last. In the last, it is written 3 into 1. 3x1, so can I write 3x1 as 10 to the power of 0 or not? So all the numbers, 2x10 to the power of 5, 4x10 to the power of 4, 7x10 to the power of 3, 9x10 to the power of 10, 8x1 and 3x10 to the power of 0, will it be or not? Because when 1 is required, 1 is the power of 0 of anyone. So if we make anyone 10, then what will be the power of 10? Will it be 1 or not? So if you ever get a very big number, then as you get a very big number, then there is a standard form to write it. What is that standard form? Assume that the sun is located at this much distance from the center of the Milky Way. The number of the stars in this area. These numbers are not convenient to write and read. To make it convenient, we use the power and observe the following. polling. Observe the following, if you have any number in your life, like 59, if we have read the decimals, can we write 59.0? Now, pay attention, we have to write it in the form of an exponent. Exponent has a standard form and we have to stick to that standard form. What does that standard form say? What did I do to this decimal? I shifted it to one place to the left. As soon as we shift one place to the left, it is written as 10 to the power 1. Or when required, 5.9 into 10 is equal to 59. Now, if I write 590.1, then how many places have we shifted the decimal to the left? Two places. So, we can write this as 5.9 into 10 to the power 3 when required. What is written here? 5, 9, 2, 0. This is decimal. So, how many places are we shifting decimal? We are shifting it to 3 places. If we shift it to 3 places on the left, then what is written? 10 to the power 3. Then, similarly, this decimal will be written here. Shifted it to 4 places on the left, then what will happen? 10 to the power 4 and so on. So, here, you see one thing carefully. Give a very close observation here. That here, this value 5.9, something is happening something is happening so this value which we are writing again and again, is this value always between 1 and 10 or not? I am trying to make it like this again and again that its value will always come between 1 and 10 or not? between 1 and 10, what does it mean? starting from 1, it is only between 10, means we don't have to take 10 this should be what? that is 9.3, 9.4 but we can't write We can't write something. So this is called Standard Form and listen carefully We have expressed all these numbers in the standard form And the number that can be expressed in a decimal between 1 and 10 Between 1 and 10 including 1 You will include 1 but not 10 Multiplied by the power of 10 Such form of a number is called as what? Standard form. Isse hum bolte kya beta? Standard form bolte hain. And this is very important. Kyuki bohot saari bachcho ko standard form hi nahi likhna aata hai. Kyun? Kyuki standard form kya hota hai? 1 se leke 10 tak ka pehle number likho. Koi bhi number likho. Into 10 to the power chalega. To ye kaise likhenge? Dekho. Abhi samajh me aaye? Dekho. Express the number appearing in the following statement in the standard form. If I give you a small number, this is a very big number, we will solve this later. I wrote 4301, write this number. How will we write this in standard form? Put the decimal here. Now where do we have to reach here? We have to reach from 1 to 10, so how many places will we take our decimal to the left? We will take it to 3 left. So how much will it be? 4.301 into 10 to the power of how much will it be? Simply 3 will be. I will do one more. I wrote 431, 421. So, we have to keep 421 in standard form. So, between 1 and 10, we have to make 4 point something. So, this is your decimal 0 and this is shifted to 2 places left. So, how much will this be? 4.21 into 10 to the power 2. Will it be or not? Right? These are what examples. Let me do one more. If I say 53101. Right. Such a number is written. So if we convert this to standard form. So what is written here? Point is 0 here. Now its value should come between 1 and 10. So 5 point something will come. So we shifted the decimal here or not. How many places are left? 1, 2, 3, 4. So this will be what? 5.3101 into 10 to the power. How much is 4? This is the way you write. So let's do this question quickly. What is written here? 3, 8, 4 Once 2, 3 and this much meter seconds Right? So now I will put decimals here Here I have put decimals Now where do I have to take this decimal? I have to take it straight here Yes or no? So what is written here? 3 points Right? Now how many decimals? 8, 4 Right? How many zeros? 1, 2, 3, 4, 5, 6 6, 7, 8 Total how many? 10 to the power 8. Now tell me, dear, how much 0 is there in the right after decimal? I will write it completely like this. Now what is written here? 3.84 into 10 to the power of 8. Now after decimal, does this 0 have any value? Does this have any value? It has no value. So you can erase this part and this is equal to what? 3.84. 4 into 10 to the power 8 meter per second is your answer good to go ye aise karte kyunki decimal ke baad light mein kitne bhi zero lagao ya mai bolu 4.2 ya mai bolu 4.20 ya mai bolu 4.2000 they are what almost same to decimal ke baad jitte bhi zeros hai ye wale kya hongi iske neglect kar sakte hai right coming to your next question isko phir se convert kado speed of the light in the vacuum to ye kitta hoga pitta fatta fatta bolu Who will say with me? We will put 0 here. So if we want to take it between 1 and 3, then we will simply jump here. As we jumped here, then what will be 3 point? How much is 0? 1, 2, 3, 4, 5, 6, 7, 8. So how much is this? That is 10 to the power 8. If we put 0 here 8 times, 3, 4, 5, 6, 7, 8. There will be no value of this. so can i write that 3 x 10 to the power 8 meter per second or not yes or no if there is no value of this then you can directly from this step to this step you can skip that right coming to your this question what does this question say is that the diameter of the earth is given as what so what is written here 1 2 7 5 6 3 times 0 so here it is written as decimal now where we have to take it by jumping it is simple we have to take it here how much jump it is 1 point now see we will write the value of this that is 2756 so likhenge ek baar 30 into 10 to the power 1 2 3 4 5 6 7 to 10 to the power 7 hoga ki nahi hoga but is zero ki kya hogi koi value nahi koi bhi value nahi to just write your answer as what 1.2756 into 10 to the power 7 meter is your answer so yes dear hopefully you people have understood this concept and the topic really very well because aaj humne bohot saare questions ki agar ma'am ke saath apne saare questions along with solve kiye hai and you got all the stars and you understood the standard form laws of exponents and powers exponents kya hotay hain to write in the chat box that i understood the concept really very well and and and and and chalo bhai humne milte apne next chapter mein tap tak ke liye tata see you and bye bye

Hello kids, how are you? I am Sakshi Kishorewal, your mathematics mentor, your teacher, your guide. So today we have brought a new chapter on your demand, which is Exponents and Power.

Now we will understand Exponents and Power very easily. And if you understand this concept well, then 8th standard is like this. I repeat that this statement is said in every lecture.

Yes, I tell you every lecture because this 6th, 7th, 8th are so basic building blocks of your life that wherever you get hold of it, things start to run very smoothly. That's why I say this thing. So, we will start today's chapter, Exponents and Powers.

So, to start this, what does ma'am say first? Copy or paper or pen. ready rakhna hai ma'am aaj bohot saare questions karayenge jaisa har baar karati hai to aaj hum log jitte bhi questions karege wo saare questions ko aapko kya karna hai apni copy mein ma'am ke saath solve karna hai aur aapko apne aapko ratings dena hai aur kya likta hai jaisa aap chat box mein likte ho ma'am i am a 7 star i am a 4 star i am a 5 star i am a 6 star kid write that in a chat box so let's begin with today's class that is what Topic to be covered.

What are we going to cover today? Exponents and powers, laws of exponents and expressing the large number in the standard form. To be very honest, to be very honest, kids, that all these topics, this topic, this topic and this topic, we will teach you in 7th, we will teach you in 8th and we will teach you in 9th. But its forms change little by little but basics never change.

On basics, once you get a command, you are like, oh. I can do this right so this is the way of doing so First thing tell me one thing that what is the need of exponents and powers I will tell you all the other things that what is the same of exponents and powers We will tell that too First thing why is the need of exponents Now I said do you know the mass of the earth is like 590000 kgs Can you read this number are you able to read this or not Or I say that mass of Uranus is this Now tell me which is greater mass? So what will you do?

Count the digits. We know how to count the digits. But not counting the digits. Assume that this has equal number of digits. Equal and equal number of digits.

So first of all you are able to read it. First of all to read it you have to 5, 7, 5, 9, 7, 0, 3 times 0, 4 times 0, then this this this this this, 0. This is the way you say it. Now you will say that we will add other things like million, trillion and so on.

But it doesn't sound good, right? It seems to be really cumbersome stuff. So what we will do is we will learn a new format to write these big numbers in the exponents form. So today's class is on the topic of if you ever get big numbers in your life, then what can we do with big numbers?

we can write it in shorter form and it is much much easier to compare it now you know that Uranus is very big to earth now you will say that you taught me geography I know that Uranus will have more mass to the earth comparison but now I tell them to read it so is it easy to read? do you find it easy to read the mass of the earth and the mass of Uranus? simply no ma'am So, this is how our... what happened?

Introduction of this chapter happened that is what? Exponents and powers. Now which field is this exponents and powers? Let's see what is this field?

Right, so what is exponents? Whatever is the large number, we write this in the shorter form. For example, I have written 8 cube, what do we read this?

8 to the power 3. Now what is the meaning What does 8 to the power 3 mean? Look, whenever we... multiplied by 3 times. So, what we multiplied? 8. The one we multiply by 3 times, we call it base.

How many times we multiplied? 3 times. The number of times we multiply, we write it up here. That is known as what? Exponent.

So, basically, if I tell you that 2 x 2 x 2 x 2 x 2. Abba Tov! How many times is 2 multiplied? 1,2,3,4,5 So what will be the base? Who are we multiplying?

2 So we are multiplying 2 This is your base or not? How many times are we multiplying? 5 times So this is your exponent Yes or no? The one we are multiplying, the one we are multiplying That will be the base And how many times are we multiplying?

That is the exponent Is this concept clear or not? Now how do we read this ma'am? We read this that is base to the power. We read this that is 8 is the base, 3 is the exponent and 8 cube is the exponential form of the 5 to the power that is form of 512, right?

So, now let's read it or we read 8 cube or 8 raised to the power, what we read? We read 3. How much power we have applied on 8? 3 powers, right? That is known as what?

8 raised to the power 3 or we say that 8 cube, right? When we have ever, now listen to me one more thing. Let's see here. This can be read as what? 8 raised to the power of what?

Beta 3. Now, ma'am, you will think that, ma'am, here, let's assume you have 6 cubes written. Now, what is 6? Come on, come on.

What is 6? This is the base number. What is 3? It is your exponent.

And here, look, here it is written, the big number. The number multiplied. How many times have we multiplied this?

That is what? Beta, we say this is known as best. Now, let's assume, if it is written in front of you, 12 into 12. Now what will be written here?

Will we write 12 to the power 2 or not? Or 12 raised to the power 2? Now what is 12?

12 is bigger But who will we multiply? This will be your base and 2 will be your exponent Now, Is exponent and power the same? No, there is a slight difference in this What is the slight difference?

What is exponent? How many times did you multiply 6? you that is what beta teen bar that is your exponent but you poor a joke Tom hey yeah Joe poor a term with a high AC both a half power the power key definition kia Houthi a the base and the exponent together matlab base or exponent ko job poor a little a that is known as what beta power so agar up case I'm a cubby as a little yellow house six to the power to yellow house six or yellow house six to the power for my book cheese sick of you Whenever you write power 2, then the way to read power 2 is called 6 square.

That is we say this is a 6 square. Here 6 raised to the power 2 is not called. We are specific in 2 and 3 because 2 is called square and 3 is called cube.

And as 4, 5, 6, 7 comes, we put raise there. What will we call this? Here 3 is power, so what will we write here? Its exponent is 3, so what will we write? 6 cube.

Now what will you write here? Here its exponent is 4. So we will write 6 raised to the power 4. Suppose you have 6 to the power 10. How much is the exponent in 6? 10. So how do we write this? We write 6 raised to the power 10. So basically we learnt that Exponent has a base and the base of exponents and power The more you multiply it, the more your exponent is And this whole thing is called power We call the whole thing power Now let's do a quick question I said express 256 as the power of 2 So do simple prime factorization which we have been doing since childhood Chalo! Whatever you do with me or whatever you do with me first tell me Factor 256 So what will be the prime factor of 2?

128 Then we will do it with 2, that is 64 Then we will do it with 2, that is 32 Then we will do it with 2, that is 16 Then we will do it with 2, this is going to be 8 Then we will do it with 2, this is going to be 4 Then we will do it with 2, that is 2 And this is 2 and from here how many times? 1 Now how many times can we write 256? How many times?

1,2,3,4,5,6,7,8 times or not? 1,2,3,4,5,6,7,8 times If it was 10,11,12,15 times then how would you feel? Do we have any shorter form?

Obviously it has shorter form So tell me, what will be its base? It is 2, so it is 2 Now what will be its exponent? How many times did you multiply? 8 times So 256 can be written as what?

2 to the power 8. Very simple. Very very simple. Right?

Now, I will tell you which one is greater. 8 to the power 2 or 8 square and 2 to the power 8. Which one is greater? Tell me a simple thing. Now tell me.

What is the meaning of 8 square? What is the meaning of 8 square? Say it fast. Say it fast.

Whoever writes before me, Ma'am, my question number 2 is before you. Before you. What is the meaning of 8 square?

8 into 8. That is what? 64. What will we call this? 8 square.

We can also say 8 raised to the power 2. but 8 square sounds little good and actually everyone is familiar with it right Now what does 2 power 8 mean? 2 times 2 is 8 times 2 times 2 is 3 this is 4 this is 5 this is 6 this is 7 and this is 8 Now we have just taken 2 power 8 in the previous question That is what? 256 So it is a simple thing It is a simple thing That is 256 is what? Greater than what?

256 is greater than that is what? 64. So 2 to the power of 8 is greater than that what? 8 to the power of 2. Answer.

Yes or no? Very easy peasy, lemon squeezy, right or not? Now, coming to next question.

Now, expand. Now, it is written expand a cube b square. What did we read?

What did I read? Listen to me. a cube into b square, right? Then I wrote a square into b cube. This is written b square into a cube.

and it is written as b cube into a square means when power is 3 then what word we will say? cube if power is 2 then what we will say? square so first one expand are they all same?

see now tell me one thing before this we have read a chapter what chapter we had read? before this what we had read? that is algebraic expression in algebraic expression we have read like terms what we had read in like terms?

we had read like terms that We will write the factors of all the numbers In factors, we will see that all the variables We did not talk about numerical factors We only talked about variable factors If the variable factors are same If it has 2x and 2x It has y and y Then these will be like terms Yes or no So we have to do the same If you look at this question carefully, then what is written here? a cube b, b square, means a is 3 times and b is 2 times. So, look at this, a is 3 times and b is 2 times.

So, is a 3 times and b is 2 times in this also? So, these two will be same. Then look at this, a square b cube, means a 2 times and b 3 times.

So, in this also, say a 2 times and b 3 times, is it not? So, these two will be same. You did it here only.

You did the question here only. For this you don't have to do this also. Expand this, do this, do that.

But we will do it. We have asked the question, we will solve it. So what is said? Come on, let's solve it quickly.

So what is the meaning of a cube b square? Like we did in the last class. a into a into a into b into b. Right? Then what is written?

a square b cube. So how much will this be? a into Right?

Then what is written? b square a cube. So how much will this be?

b into b into a into a into a. Yes or no? Then what is written? b cube a square.

So what is written? b into b into b into a into a. So which one is same?

This one is same. Right or not? So can we say that a cube b square and b square a cube are same? Yes or no?

And which one is same? This one and this one. That is a square b cube. And b cube a square are what? Same or not?

Simply same. Yes. Shoo shoo.

Kataam. Yes or no? Very very easy.

Chalo. Express the following number as the product of its prime factor. Dekho bhai, main tumhe jaan bhoot ki bohot saare questions karaati hu. That's why my video go little longer. Main chahun toh aapko bohot kam questions kara sakte hu.

Toh jabab questions... questions then only you will able to practice. So till now all the questions that you have done are you doing in copy making or not? If you are doing then write in the chat box ma'am I am solving with you. Some children write ma'am I do the questions along with you in the chat box that is really heart touching that yes you children are studying with us.

Right so what is written as the factor of prime factor. So before me who will write 72? Write that I did the prime factor of 72 before you. If we do prime factor of 72, then it will be 36, 18, 9, 3, and 1. So how can we write 72?

We can write 72 as 2x2x2x3x3. So how many times 2 came? 3 times.

And how many times 3 came? 2 times. So we can write 72 as 2 cube and 3 square. When needed. Second question, factor 432. So, before me, who will do it?

Write it in chat box that I did it before you. So, let's do a race. Let's do a race. So, how much is 432?

So, we have done prime factor. So, how much is 2? 216. Then, how much is 2? 108. Then, this will be 2. This is what? 54. 2. That is what?

27. Then, this is 3. 3 to 9, then 3, then 3 and then 1. Right or not? So what can we write 432? 432 can be written as what?

How many times? 1, 2, 3 and 4. How many times? 1, 2 and 3 times. So this can be written as what? 2 to the power of 4 into 3 to the power of 3. That's it.

Very easy peasy or not, right? Now coming to your next question. Exponents of negative number, listen very carefully.

Listen very carefully. Look, I had taught you this in integers. If you have seen my video in integers, then I had taught you this there too.

But I had told you one thing there, that if negative is more... times multiply karte to answer ki aata beta or data mother negative at a or negative number ko agar may even times multiply karte you to answer ki aata beta positive may at a to see in thing applies over here with the exponent job many bola to marry bar snow German integers may pariah kha many lakota minus 1 into minus 1 into minus 1 the minus cook it in a bar multiply kare take that is what negative was multiplied by what odd times or not yes on times means we didn't read exponents there. So now can we write it like this? 1 to the power 3? Yes or no?

Did I teach this thing 1 minus 1 multiplied by odd times and even times or not? So when we said odd times there, can I call it power 1 by 3? And how will the answer be? Will there be a negative answer or not?

Remember, the same thing which I taught you in integers, The way of speaking is different. If I write minus 2 into minus 2 into minus 2 into minus 2. So, what I had studied in integers. What is happening here? Minus 2 is multiplied 4 times. Is it even times or not?

Or I can write it like this. Minus 2 power 4 or not. Yes or no.

So, the power of negative. If it was even times, then remember. Negative multiplied by even times give you answer as what?

Positive or not. Remember, this ma'am has taught you or not. This ma'am has already taught you. Then after that, today I am just telling you a method that we can think of it this way.

So this means that, this means that, whenever you have, like suppose I gave you a question, minus 2 multiplied by minus 3 multiplied by minus 3 multiplied by, 2. Let me give you a question. Remember, what did we learn? 1 times negative, 2 times negative, 3 times negative. Yes, isn't it?

If 3 times negative comes, remember, how did we learn? We learned like this. Look, we had said earlier that 3 times negative. So, if negative is 3 times, then the answer will be negative.

Then what did we multiply? 2 x 3 x 3 x 2. So, 3 x 3 is 9, 9 x 2 is 18, and 18 x 2 is what? Minus 36. Will its answer come or not? Remember it with simple integers This chapter is a very good chapter If you have command on integers then first And if you know algebraic expressions then this chapter is also like this It is easy to understand So this means If ma'am writes in front of you Minus 2 to the power 57 So will its answer be negative or positive Its answer will be 100% negative Because the power of negative is odd. Yes or no?

So we saw that if the power of negative is odd. Or if I say that I have multiplied negative by odd times. Yes or no?

So the answer to this is negative. And if I say that the power of negative is even. Or if I say that I have multiplied negative by odd times. So the answer to this is positive or not?

Simple thing. So, how will be the power of minus 2, 57? Will there be a negative answer or a positive answer?

It will be negative. We just asked whether it will be negative or positive. Now, I asked, what will be the answer of minus 3, 104? Will there be a positive or a negative answer?

So, how will the answer be? It will always be positive. It will always be positive. So, keep this in your mind that some points to remember means, If the power of negative is odd number, then it will always give negative answer. If the power of negative is even number, then it will always give positive answer.

Now, if I write a cube b square, then it is equal to a square b cube. Remember like terms. Are these like terms?

No, they are not like terms. Then I said that a square b cube is equal to b cube a square. So, what is this?

Is it a light term or not? This is like term, this is like term, this is like term. So, that's why this chapter is put so low in your NCRT book.

Because you are expected to know integers. Till when you will know algebraic expression When you will read all these things properly Then you will understand what will happen It is a game of little things Let's move on to the next thing Workout So what is written here Workout 1 to the power 5 Minus 1 to the power 4 Minus 1 to the power 5 So what is written here 1 to the power 5 Someone's power is positive power 5 three, four. and this 5 will be 1 minus 1 to the power 3 now minus is minus to the power odd so minus to the power odd will be negative 1 or not simple now I said minus 1 to the power 4 so negative to the power even will be plus 1 simple plus 1 what is written minus 10 to the power 3 now see first thing what is written minus 10 to the power 3 if you open this open this So what is written? Minus 10 into minus 10 into minus 10 is written.

So minus is 3 times, so the answer is minus. And how many times is 10? 3 times, so 1000 is given. Here I will tell you in short. So first thing is minus 10 to the power 3. So its answer will be 100% minus.

Negative to the power 3 is what? Negative to the power odd is negative. Now how much is 10 to the power 3?

So we have to multiply 10 3 times. It is very easy to multiply 10 3 times. So minus 1000 is your answer. Now what is written?

Minus 5 to the power of 4 Now see what is written? Minus 4 into minus 5 into minus 5 into of minus 5 Right or not? Now tell me one thing How many times is negative? 1,2,3,4 So the answer will be positive Now 25 into 25 How much will it be? 625 or not?

Or we could have written it like this Negative to the power of even is positive And 5 to the power of 4 is 5 into multiply it and it will be 625 is your answer so without opening it you could have answered the question now coming to laws of exponent listening very carefully is very easy first thing is that do you have base clear when I am starting laws of exponent before that you write in chat box before I starting my laws of exponent you write that ma'am before laws of exponent I have clear base I have clear exponents and power When I have clear like and unlike terms When you write this much in the chart box Then you will understand it very quickly So first look Laws of exponent of the what This is called addition If you have I tell you 2x2x2 What is written here? 2 cube is written Yes or no? Ok I write 2 to the power of 4 So what is written here?

2 x 2 x 2 x 2 x 2 Right? Now I will tell you What is 2 to the power of 6? See, this will be 2 x 2 x 2 x 2 x 2 Ok, I will write it like this Let me explain it to you Listen to me first Then you will understand what is written above Now see I am multiplying these two So what will be this?

2 to the power 2 into 2 to the power 4 How many times is this? Multiply 2 to the power 2 2 to the power 3 This is 3 Into 3 And into 2 into 2 into 2 into 2 into 2 Right? Now tell me How many times did 2 come?

1, 2, 3, 4, 5, 6, 7 Did 2 come 7 times or not? This is equal to what? 2 to the power 7 And here what was written?

2 to the power 3 into 2 to the power 4 So now here you see Is your base same? And what is the base in multiplication? What is the base in multiplication?

So here, what is the power of 2? 2 to the power of 7. So could we have written 2 to the power of 7 as 3 plus 4? Yes or no?

So this means that if ever in front of you the base is same, if we multiply the powers which have the same base, then we add the exponents. What does it mean? That if in front of you, 2 power 3 and 2 power 4 are multiplying What is the base of both? Is the base same or not? If the base is same, then both the exponents are simply added And we have learnt this logic just now So this is its general form If there is a power m multiplied by a power n Then what happens in this?

The exponents of both are simply added If I give you an example Tell me quickly 8 to the power 3 plus 8 to the power 4 is how much? Say it quickly. 8 to the power 3 plus 8 to the power 4 is how much? Say it before me. How much is 8 to the power 3 plus 4 which is equal to what?

8 to the power 7. Simple. Very simple. Now it comes that when you both I wrote 2 to the power of 4. Have you seen this?

2 into 2 into 2 into 2. Now what I am doing is, I wrote 2 to the power of 3. So this will be 2 into 2 into 2 into 2. Right? I am doing 2 to the power of 4 divided by 2 to the power of 3. So this will be 2 into 2 into 2 into 2. And what is written here? 2 into 2 into 2. So this 2, this 2 cancel, this 2, this 2 cancel, this 2 and this 2 cancel. So what is the answer? 2 to the power 4 divided by 2 to the power 3 is equal to what?

2 to the power 3. Now if 2 is written, can I write it as simple power 1 or not? Can I write it as 2 to the power 4 minus of 3 or not? If 1 is required, can I write it as 4 minus 3?

So if you have two exponents or two powers and both have a base... same and both are in division then powers simply subtract. So if we divide the powers which have, both have powers, we are dividing and if their base is same then subtract the exponent.

Pick up the exponent and subtract. So I said that is its base same, its base same. Its power, its exponent is different.

So what we will do is subtract these two exponents. Now here it is said that the exponent of your numerator is greater than your denominator. Right, say an example.

If I say 8 to the power 4 divided by 8 to the power 3, then how much will it be? Say it quickly. Can I write this as 8 to the power 4 minus 3 which is equal to what? 8 to the power 1 which is equal to 8. Yes or no?

Look at the third law. Third, quickly write it with me too. What is written?

If we have to take the power of the power then we have to multiply the exponents. So now see, I wrote, I am changing the color, right? I wrote 2 to the power 3, right? 2 to the power 3 to the power 2, yes or no?

I wrote this. So what does this mean? This is the base inside, this is the whole base. So what is written here?

2 to the power 3 into 2 to the power 3, written twice or not? Yes or no? You tell me one thing, if I hide it like this, then will this whole 2 to the power 3 be the base or not? If 2 power 3 is the base then what is written here? We have opened it twice Now see here its base is same and here its base is same So what will be the powers?

2 power 3 plus 3 which is equal to what? 2 power 6 Now if it is required What is required? I could have written 2 power 3 into 2 or not So what will be 2 power 3 whole to the power 2?

Simply multiply both of them If I ask you a question Here, we are opening the answer of a to the power of m So the answer to this will be by multiplying both of them So if I tell you that 8 to the power of 3 into 4 So what is written here? This is your base, so how many times will you open the base? 8 to the power of 3, will you open it 4 times or not?

8 to the power of 3 into 8 to the power of 3 Yes or no? Now, the base of all is the same What is the multiplication of 3 and 4? powers will be added so 8 power 3 plus 3 plus 3 plus 3 what will happen?

so how much will it be? 8 power 12 or not? which is equal to what?

8 power 3 into 4 or not? simply yes or no? so what to do? if these two are on the base and 2 powers are on the multiply then what to do with simple powers?

multiply them what to do? multiply powers so this is your what? third law now coming to your fourth law what does the fourth law say is that How to multiply the powers with the same exponent? If we have to multiply the power where the base is different, but base is different. Base where the base is different, but the exponents are same, then we multiply the base.

What is he saying? Look, he is saying that when the base is different, and power is same. Like I said, 2 power 3 and 4 power 3. Yes or no?

Is its base same? Sorry, its base is different. I will subtract 4 power 3 and make it a little bit 5 power 3. It will be easier.

You will understand better. So, its base is same, different and its base is different. But will both the exponents be same or not? Yes or no?

So, what is written here? I can write this as 2 into 2 into 2. And what can I write 5 as? 5 into 5 into 5. Now, what am I doing? I am doing pairing.

So, I will pair this and this. There is no difference in multiplying. So I wrote 2x5 as one pair and then 2x5 as a separate pair. Right?

And could I make this and this as a separate pair or not? So what is 2x5? It is simply 10. Then what is 2x5? 10. And what is this? 10. So what is this?

10 to the power 3. Yes or no? So when needed, is 2x5 to the power 3 written or not? So basically if your base is different and exponent is same then what happens? Power becomes separate and also becomes together So what is written here?

A power m into B power n So what will happen? Both of these multiplied and what will happen? This will be m Base is same so what will happen? M will happen For example I wrote 8 power 3 So its base is same, its base is different, not base same, base different, base different, exponent same, exponent same.

So what will happen? 8 into 4 to the power of beta 3 which is equal to what? 32 to the power 3. So if you write its opposite, sometimes it is written like this, 2 to the power 3 to the power 5, so what will happen? 5 will climb on this and 5 will climb on this.

So what will be written? 2 to the power 5 into 5, sorry 3 to the power. How much power will be 3?

It will be 5. Simple. So basically if we save the base different, the exponent same, then what will you do? You will make the exponent a corner, you will multiply both and write it as it is. So this is your fourth law. Now coming to your fifth law.

What does the fifth law say is that if you have to divide the power, see it has a lot of laws. If we have to divide the power where the base is different, is different. Base is different but the exponent are same then we divide the base. See what is written here. Listen very carefully.

It is very easy. I wrote 2 to the power 3 and what did I write? I wrote 5 to the power 3. Again I said base is different. Now what happened? Both were in multiply.

Base was different. Exponent was same but both were in multiply. If they were in multiply then what to do? Multiply base and exponent will be same.

Now both of them. What is it? The base is different and the exponent is same. But how are they in division? So what is written here?

It is written 2 into 2 into 2. And what is written here? 5 into 5 into 5. So can I write 2 by 5 in one bracket? Can I write 2 by 5 in one bracket? Can I say 2 by 5 or not?

So is 2 by 5 whole power 3 when needed? Same thing is applied. That is 2 power 3 and 5 power 3. So when you multiply, So, same thing works and division works the same thing. So, when both are multiplied, multiply it and separate the exponent.

And when it is divided, write it like this. So, if I say 8 cube upon 4 cube, then how much will it be? 8 by 4 cube and this and this will be cancelled, how much will it be?

2 cube. Yes, this one. So, if I say 8 cube divided by 4 cube, then first you take out the power of 8, then 4, then you do cancellation.

So, how much work does this do? Is it long or not? and this made your calculation much much much much easier right now if you have okay if your exponent is 0 like I said 3 power 0, 4 power 0, 5 power 0, 7 power 0 then what will be the answer listen carefully it is very easy I wrote 2 power 3 divided by 2 power 3 so how much will it be 2 power base same base what did I write 2 into 2 into 2 How much is this?

2 x 2 x 2. So, how much is this cut cut cut cut cut cut cut cut? 1. So, 2 to the power 3 divided by 2 to the power 3, how much is 1? Right? Now, tell me one thing. Am I more?

Look more. Son, 2 to the power 3 divided by 2 to the power 3. Base same? Base same.

And both are base same and how? In division. So, what will be base?

Son, will exponent be subtracted or not? 2 to the power 3 minus of 3 will be or not? Which is equals to what? 2 to the power 0. to So, 2 power 3 by 3, how much is its answer? 1. Once the answer is 2 power 0. So, can we say that 2 power 0 is 1 or not?

Yes or no? So, we came to know that anyone's power, anyone's power, 7 power 0, 22 power 0, 1,101 power 0, or I say 1,05,051 power 0, its answer will always be 1. no matter what, its answer will always be 1, right? So, the power of 0 of any one, as we took it out from this, this is its proving. This is how you prove that how to get the power as.

The power of 0 of any one is always 1. So, if I say, what is the power of 0 of 8? It is simply 1. Now, I will tell you, any exponent, If I say that the power of any one is exponent 1, then what will be the answer? Will it be the same or not? So what will happen? Any number Any number with the same exponent is equal to the number itself.

What will happen? It will be equal to itself. So, a to the power of 1 is equal to what? Simply a.

So, what will be the power of 8? Simply 8. Right? Now, let's come to using. Let's do questions. Now, it's your turn.

It's your turn. So, in your turn, I will start giving stars from here. I will start.

Right? So, from here, do you understand the laws of exponent or not? First thing. If you really want to understand the laws of exponents, then write all the laws in a copy.

Write all the laws in a copy. What laws will you write? What laws will you write?

I guess I have space here. Look, we know that the power of A is m. I will write it once. What is the power of A? If the base is same and in multiply, powers add.

Right? Then we read the second. that if A is the same base and in division then powers get subtracted remember as I am saying third we read that if A is the same power m and if it is multiplied then it becomes A power m into n fourth we read that A power m into A power n base is different a to the power m into b power m.

Based different exponent say multiply me. So, what will happen? a into b to the power.

How much will be beta m? Then we read fifth. If a power m base same and both are in division and exponent same. So, how much is this? a by b to the power m right.

Then we read sixth. Someone's power is 0. Someone's power is 0. How much is beta 1? And someone's power.

That is someone's power. I am saying again and again. If someone's exponent is 1, then the answer to that is number itself.

So, we have read all these things till now. And these are laws of what? These are laws of exponents which we are going to use in the coming questions.

And let's see how quick you are. Okay, use the laws of exponents and simplify and write the form in the exponential form. So, what is the first one?

Look, the first one is base, base, base, same. Base, same. So, which laws will we use here? that is a to the power m into a to the power n is equal to what?

a to the power m plus n. Right? So, how much will this be? 3 to the power 2 plus 4 plus 8. So, how much will this be?

3 to the power 10 or 14. Will it be or not? Leave your answer in like that. If this is correct, then give 1 star.

Right? Coming to your next question. What does the next question say?

Here, look. Base is same in both divisions. That is, what will we write here?

a to the power m divided by a to the power n. So, what will happen? Exponents will be subtracted.

So, what is written here? 16 to the power 15 upon 6 to the power 10. Which is equals to what? 6 to the power 15 minus of 10. Which is equals to what?

6 to the power 5. That's it. This is 2 stars. Quickly.

Quickly. Very quickly. Now, coming to your third question. Now, see. First thing is this division.

Now, see here. Its base and this base are not the same. Here, 5 to the power 2 is there.

And here, it is only 5. So first of all we will simplify this So we know that A power m multiplied by A power m is equal to A power mn So if we simplify this then it will be 5 power that is 2 multiplied by 3 divided by 5 power 3, so this is equal to 5's power this will become what 5 to the power 6 divided by what 5 to the power 3 yes or no? now what is in this? both the bases are same and what are the exponents of both?

both are in power and divided so what will be the exponents? that is 5 to the power 6 divided by 5 to the power 3 which is equal to what? 5 to the power 6 minus 3 which is equal to what?

5 to the power 3 now 5 to the power 3 is a very small number which we multiply and tell we have to leave it in exponential form leave it leave it don't tell the answer that is 5 to the power 3 is your answer right? Coming to your fourth part. What will we do in this? Look, what will we do in this?

Here, which one of these we will use? That is a to the power m into n which is equal to what? a to the power mn we will use. So, how much is this? 3 to the power 4 into 3. That is 3 to the power 12. What will we do with the first question?

We will give here, 2 star was done. Here, 3 star. Right? We will do this question 4 star. Write 4 stars.

Now next question. Simplify. Quickly simplify. Now see, when you have to simplify this question, in the question of exponents, open your ears and tie a knot in your mind. Tie a knot in it.

Whenever you solve the questions of exponents, always make a common base. What do you make? Make a common base. If you solve this question before me, then give yourself 10 stars. Literally give 10 stars.

This is a good question. Now, To simplify this, always make the base same whenever possible. Whenever possible.

Now watch. Now we will do prime factor for each one. I am doing it here. What can we write for 12?

We can write 12 as 4x3. Yes or no? If we do the factor of 12, what will it be?

2 square x3. Now remember, its power is 3. So here the power of the whole will also be 3. Do you remember or not? Then remember that this power goes to this and this power goes to this.

So how much will it be? 2 power 2x3 x3 power 3. which is equal to what? 2 to the power 6 into 3 to the power 3. We have broken 1. Now see, how can I write 9 first? Could I write 3 square or not? How much was the power of 3 there?

3 is there. And how much will be the power of 3 here? 3 will be there. We have applied power on both sides.

Now what will happen here? Both will multiply. So how much will it be? 3 to the power 6 will be there. Right?

What can we write for 4? We can simply write 4 as 2 square. There is nothing in this.

Now see, what can we write for 6? 2 into 3. Right? Now what is written there? That is power 3 and this is also written as power 3. Now if the exponents are same then what will happen? Powers will be distributed.

This will go to this and this will go to this. So which is what? 2 to the power 3 into 3 to the power 3. Then what is written? 8. We can write 8 as 2 into 2 into 2. Now do this.

That is 2 cube. So what will be 8 square? So here also we have put 8 square. Which is equal to what?

These two will multiply. That is 2 into 3 which is equal to what? 2 to the power 6. Now what is written in the last? 27. So what can we write for 27?

3 power 3. Can we write or not? Now you see carefully that I have written all the numbers in the form of a new exponent or not? And what is the base of everyone?

2 or 3 is coming or not? What is the base of everyone? 2 or 3 is coming. So first thing, see how will we solve this?

How will we solve? 12. We could write 12. We could write 12 cube. 2 to the power 6 into 3 to the power 3. 9 to the power of 3 is 3 to the power of 6 And 4 to the power of 2 square Did you get it?

Now, what could we write for 6 to the power of 3? That is 2 to the power of 3 into 3 to the power of 3 Right? Now, what could we write for 8 square?

2 to the power of 6 And 27 to the power of 3 square Now, what should we do? In numerator and denominator, first do the base same Right? Now, see, is this base and this base same?

Yes or no? So if the base is same then what happens? Adds And is this base and this base same? So what will be the powers of these two?

Adds So what can I write? 2 to the power of 6 plus 2 into 3 to the power of 3 plus 6 Yes or No? Whole divided by In this, it is 2 and here it is 2 Yes or No?

So how much will it be? 2 to the power of 3 plus 6 into 3 to the power of this and this is it or not? So 3 to the power of 3 plus 2 Now how much did it become?

2 to the power of 8 times 3 to the power of 9 whole divided by 2 to the power of 9 times 3 to the power of 5 now what will be the next step? now their base is same and their base is same if base is same and both powers are in division then exponents get subtracted So, how much will be the answer of this? 2 to the power of 8 minus of 9 into 3 to the power of 9 minus of 4. Which is equal to what? 2 to the power of minus 1 into 3 to the power of 4. Leave your answer like this. That's it.

Correct. And if you get this answer right. Ya, ya.

Many children will write it like this. That is, they will write it like this. I don't have space, I guess. Some children will get the answer.

power 4 upon 2 to the power of 9 minus of 8 Means he has reduced this 8 to the power of 9 So now the answer will be 3 to the power of 4 upon 2 to the power of 1 So both the answers are right You can quote any of your answers Yes or no So if this is correct Then please give yourself at least A 5 to 6 star 1, 2, 3, 4, 5, 6 and 7 7 star 2 Now the next question is Simplify Now what word is given here? Simplify Now simplify this, this is comparatively easy Here what we have to do is, as we used to study algebraic expression In algebraic expression we used to multiply number by number So this is the number and this is the number. So what is 2 cube? 2 cube is simply 8. What is written here? A cube.

Right? What is written here? 5 and what is written here?

Into a to the power 4. Yes or no? Now multiply the number with the number. So if we multiply the number with the number, then what will happen?

8 into 5 is 40. Right? Now what is here? Its base and its same, and what are the exponents?

The base of these two is same. So what will be the exponents? Beta beta powers don't have power in multiplying And what will be the exponents? Simply add So into a to the power 3 plus 4 Which is equal to 40a to the power 7 This is your 9 So for this we will give only 5 star 7 star was that question Right?

Good to go? Good to go? Good to go? Right? Now one more question Simplify You guys do this question quickly Do it like that Break it Break it by lifting everyone See, 2 is already break, so what can we write?

2 to the power 1. 3 is already break, so what can we write? 3 to the power 4. 2 to the power 5 is already break, that is 2 to the power 5. What can we write for 9? We can write 3 square. And what can we write for 4? 2 to the power 2. And what will be its square?

That is 2, which is equal to what? 2 to the power 4. Yes or no? Pick up everything and keep it in this. So, how much will it be? 2 to the power 1 into 3 to the power 4 into 2 to the power 5. divided by 3 square into 2 to the power of 4. Yes or no?

Now this and this base are same. So how much is 2 to the power of 1 plus 5 into 3 to the power of 4? Divided by 3 to the power of 2 into what? 2 to the power of 4. So how much is this? 2 to the power of 6 into 3 to the power of 4. Whole divided by 2 to the power of 4 into 3 to the power of 2. Is the power of these two same?

Right or not? What are the powers of these two? Sorry, what are the powers of these two base and division? So, the exponents will be subtracted. So, what will be the answer?

2 to the power of 6 minus 4 into 3 to the power of 4 minus 2. Which is equal to what? 2 square into what? 3 square.

So, what is 2 square? 4. And what is 3 square? 18. So, what is 18 to the power of 4?

36. 72 is your answer. For this, 6 star. 4, 5 and this 4. Right. Now, say.

true or false and justify your answer. Quickly, what will be 10 into 10 to the power 11? 100 to the power 11, true or false?

Quickly say it. If we simplify this, base same, then what will be the powers? How much is this? Power 1. So 10 to the power 1 plus 11 will be what? 10 to the power 12. So can this ever happen?

No, it can't. Simply false. Simply what happened?

False. Right? Now coming to your next question.

It says that 2 cube is greater than that of 25. So how much is 2 cube? 8. And how much is this? so this is what?

false now third says 2 to the power 3 into 3 to the power 2 is what? 6 to the power 5, this is wrong, neither the exponent is same nor the base is same so multiply this and see, so 2 to the power 3 is what? that is 8, 2 to the power 3 and this will be how much?

3 to the power of 2 is 9 so 9 into 2 is how much? 8 into 9 is 72 now 6 into 6 into 6 into 6 into 6 5 times so 6 into 6 is 36 36 into 6 is how much? this value is 216 so this value will never be equal then after this 216 into 6 into 6 so this value is very big so this also will be false simply false coming to the next part 3 to the power 0 and 1000 to the power 0. So, what is the value of any power 0?

How much will this be? It will be 1. How much will this be? It will be 1. Any power 0 is what? 1. So, this is what? 2. Simply 2. Right?

Now, till now, as we had talked in the starting, that the mass of the earth and the mass of the Uranus was a very, very, very, very large number. So, ma'am, till now, you were teaching these laws of exponents. We are going to talk about that only If you have any number written For example this number We are writing it as 247,983 So we write 2 x 1 lakh 2 x 4 x 10,000 7 x 1000 Now one more thing Can I write 10 to the power of 5 or not?

Can I write 10 to the power of 4 or not? How do we write 100? 100 can be written as what?

10 into 10 which is equal to 10 to the power 2. 1000 can be written as what? 10 into 10 into 10 which is equal to what? 10 to the power 3. So if I say I want to write 10,000, then how many times do we multiply 10?

10 into 10 or into 10. So 4 times 0, how much will it be? 10 to the power 4 or not? So could we write any number in 10 to the power or not? Now look at the last.

In the last, it is written 3 into 1. 3x1, so can I write 3x1 as 10 to the power of 0 or not? So all the numbers, 2x10 to the power of 5, 4x10 to the power of 4, 7x10 to the power of 3, 9x10 to the power of 10, 8x1 and 3x10 to the power of 0, will it be or not? Because when 1 is required, 1 is the power of 0 of anyone. So if we make anyone 10, then what will be the power of 10? Will it be 1 or not?

So if you ever get a very big number, then as you get a very big number, then there is a standard form to write it. What is that standard form? Assume that the sun is located at this much distance from the center of the Milky Way.

The number of the stars in this area. These numbers are not convenient to write and read. To make it convenient, we use the power and observe the following. polling. Observe the following, if you have any number in your life, like 59, if we have read the decimals, can we write 59.0?

Now, pay attention, we have to write it in the form of an exponent. Exponent has a standard form and we have to stick to that standard form. What does that standard form say?

What did I do to this decimal? I shifted it to one place to the left. As soon as we shift one place to the left, it is written as 10 to the power 1. Or when required, 5.9 into 10 is equal to 59. Now, if I write 590.1, then how many places have we shifted the decimal to the left? Two places.

So, we can write this as 5.9 into 10 to the power 3 when required. What is written here? 5, 9, 2, 0. This is decimal. So, how many places are we shifting decimal? We are shifting it to 3 places.

If we shift it to 3 places on the left, then what is written? 10 to the power 3. Then, similarly, this decimal will be written here. Shifted it to 4 places on the left, then what will happen?

10 to the power 4 and so on. So, here, you see one thing carefully. Give a very close observation here. That here, this value 5.9, something is happening something is happening so this value which we are writing again and again, is this value always between 1 and 10 or not?

I am trying to make it like this again and again that its value will always come between 1 and 10 or not? between 1 and 10, what does it mean? starting from 1, it is only between 10, means we don't have to take 10 this should be what?

that is 9.3, 9.4 but we can't write We can't write something. So this is called Standard Form and listen carefully We have expressed all these numbers in the standard form And the number that can be expressed in a decimal between 1 and 10 Between 1 and 10 including 1 You will include 1 but not 10 Multiplied by the power of 10 Such form of a number is called as what? Standard form. Isse hum bolte kya beta?

Standard form bolte hain. And this is very important. Kyuki bohot saari bachcho ko standard form hi nahi likhna aata hai. Kyun?

Kyuki standard form kya hota hai? 1 se leke 10 tak ka pehle number likho. Koi bhi number likho.

Into 10 to the power chalega. To ye kaise likhenge? Dekho.

Abhi samajh me aaye? Dekho. Express the number appearing in the following statement in the standard form.

If I give you a small number, this is a very big number, we will solve this later. I wrote 4301, write this number. How will we write this in standard form?

Put the decimal here. Now where do we have to reach here? We have to reach from 1 to 10, so how many places will we take our decimal to the left?

We will take it to 3 left. So how much will it be? 4.301 into 10 to the power of how much will it be? Simply 3 will be.

I will do one more. I wrote 431, 421. So, we have to keep 421 in standard form. So, between 1 and 10, we have to make 4 point something. So, this is your decimal 0 and this is shifted to 2 places left. So, how much will this be?

4.21 into 10 to the power 2. Will it be or not? Right? These are what examples.

Let me do one more. If I say 53101. Right. Such a number is written. So if we convert this to standard form.

So what is written here? Point is 0 here. Now its value should come between 1 and 10. So 5 point something will come. So we shifted the decimal here or not. How many places are left?

1, 2, 3, 4. So this will be what? 5.3101 into 10 to the power. How much is 4? This is the way you write. So let's do this question quickly.

What is written here? 3, 8, 4 Once 2, 3 and this much meter seconds Right? So now I will put decimals here Here I have put decimals Now where do I have to take this decimal?

I have to take it straight here Yes or no? So what is written here? 3 points Right?

Now how many decimals? 8, 4 Right? How many zeros?

1, 2, 3, 4, 5, 6 6, 7, 8 Total how many? 10 to the power 8. Now tell me, dear, how much 0 is there in the right after decimal? I will write it completely like this.

Now what is written here? 3.84 into 10 to the power of 8. Now after decimal, does this 0 have any value? Does this have any value? It has no value. So you can erase this part and this is equal to what?

3.84. 4 into 10 to the power 8 meter per second is your answer good to go ye aise karte kyunki decimal ke baad light mein kitne bhi zero lagao ya mai bolu 4.2 ya mai bolu 4.20 ya mai bolu 4.2000 they are what almost same to decimal ke baad jitte bhi zeros hai ye wale kya hongi iske neglect kar sakte hai right coming to your next question isko phir se convert kado speed of the light in the vacuum to ye kitta hoga pitta fatta fatta bolu Who will say with me? We will put 0 here. So if we want to take it between 1 and 3, then we will simply jump here.

As we jumped here, then what will be 3 point? How much is 0? 1, 2, 3, 4, 5, 6, 7, 8. So how much is this?

That is 10 to the power 8. If we put 0 here 8 times, 3, 4, 5, 6, 7, 8. There will be no value of this. so can i write that 3 x 10 to the power 8 meter per second or not yes or no if there is no value of this then you can directly from this step to this step you can skip that right coming to your this question what does this question say is that the diameter of the earth is given as what so what is written here 1 2 7 5 6 3 times 0 so here it is written as decimal now where we have to take it by jumping it is simple we have to take it here how much jump it is 1 point now see we will write the value of this that is 2756 so likhenge ek baar 30 into 10 to the power 1 2 3 4 5 6 7 to 10 to the power 7 hoga ki nahi hoga but is zero ki kya hogi koi value nahi koi bhi value nahi to just write your answer as what 1.2756 into 10 to the power 7 meter is your answer so yes dear hopefully you people have understood this concept and the topic really very well because aaj humne bohot saare questions ki agar ma'am ke saath apne saare questions along with solve kiye hai and you got all the stars and you understood the standard form laws of exponents and powers exponents kya hotay hain to write in the chat box that i understood the concept really very well and and and and and chalo bhai humne milte apne next chapter mein tap tak ke liye tata see you and bye bye

Transcript for:Exponents and Powers Overview

Transcript for:
Exponents and Powers Overview