hi guys good day it's me teacher RJ our topic for Today class it's all about zero negative and rational exponents so without further Ado let's do this topic so let's start with zero exponents now in zero exponents class this will be really easy for us to solve this one because any letter any number any equation raised to the power of zero your answer is one okay so we have a rais power of zero the answer is one that's it class easy for the zero exponents right so if you have an equation if you have a number a letter raised to the power of zero your answer is just one so let's try example Number One X rais to the^ of 0 your answer is that's correct your answer is one so the answer for number one is one that's it easy for number one right so let's try number two 3 to power of 0 multiplied by y so we we have 3^ 0 * y so if you have a number together with a variable it means multiplication so if the number and the variable are close to each other and there's no operation it means multiplication class so 3 of Z of course this is one and then our y here understood that any variable any number if you didn't see any exponent understood to be one class okay once again if you have three if you have a if you have y if you have five any number any variable there is an exponent of one that's imaginary class so we have 3 power 1 a 1 y power 1 5 ra power 1 now if their exponent is one just simply copy this number copy this letter copy this letter okay so three r one you can write that one as three so that's the same class so understood that any number any variable there is an exponent of one so we have y power of 1 so we can just simply copy y so 3^ of 0 that is 1 * y so time y so no need to do anything about y because y the exponent is one so just simply copy y so 1 * y that is y one y or Y so you can put one y that's okay but understood that there's one here for y so just simply copy y That's it plus that's the answer for number two easy right for number two all right let's try number three so this equation quantity raised to the power of Z so all of the numbers all of the equation is raised to the power of zero the answer is just one class all right that's at Four number two so so easy for numbers 1 two and three now for number four we have five to power of 0 + 3 so 5 to power of 0 that is 1 then + 3 three so that would be 1 + 3 that is 4 that's it plus all right let's try number five so 4 to the power of 0 okay 4 to power 0 that is 1 then + 8 so + 8 over 3 so do not forget we have over three so we have 4 power 0 that is 1 then + 8 over 3 so 1 + 8 that is 9 then over three so can we divide 9 ID by 3 yep 9 ID by 3 that is three so that's the answer for number five so let's try number six so we have this quantity so we have X ra power 0 + 5 so we can answer this one as put quantity X power of 0 that is 1 + 5 all right and this equation all of this equation x + 25 it is rais power of0 therefore this equation x + 25 is equals to 1 because all of this equation inside this parenthesis is raised to the^ of 0 so therefore x + 25 that is equivalent to 1 * 1 so since we have two quantities it means multiplication so once again X power 0 that is 1 then + 5 now in this second equation second quantity x + 25 is raised to^ 0 so this is 1 so we have 1 + 5 that is 6 * 1 so our answer is 6 all right that's the answer for number six let's try number seven so could you try this one class number seven and you put your answer in the comment section down below let me check if you really understand our topic so you try this one 1 12 ra to^ 0 multiplied by 1/4 and tell me what's the answer class okay you try this one and you put your answer in the comment section down below for number seven all right so let's try negative exponents so we we're done with zero exponents so zero exponents next next thing class is we will be dealing with negative exponents all right so you pause the video because I will be erasing this one we will be discussing the negative exponents all right so our next topic will be the negative exponents so just bear with me class we will be explaining this one step by step all right let's start with negative exponents so in negative exponents class if you have a raised to the power of n that is equivalent to 1 over a raed power of n and if you have 1/ a power of n that's equivalent to a ra to the power of n so we will be explaining this one class step by step so once again you need to Master Class the loss of exponents be before answering the zero negative and rational exponents because in the loss of exponents class you can also apply this negative exponents but we will be explaining this one class step by step do not be worried so a to the power of n so if you have an equation rais to a part of a negative number or negative exponent the thing that we will do is we need to get the reciprocal so example class if you have X raised to the power of -2 the thing that we will do understood that any variable any letter any number there is a denominator of one okay there's a denominator of one just get reciprocal C this one will be your numerator so this one will be your numerator and this x will be your denominator so to get the reciprocal just simply flip the equation class this x will be your your denominator and this one will be your numerator so get the reciprocal that would be 1/ X raed to the^ of two and this negative exponent will be positive so that's the thing there class let's try another example class X ra power of -3 so once again understood that any number any letter there is a denominator of one just get the reciprocal that would be 1 /x ra to^ of 3 that's it l easy right so let's try another example what if we have a number 1 over or let's have 2 ra to part of -3 so understood once again any number there is a denominator of one get the reciprocal that would be 1/ 2 ra to power of 3 this -3 it becomes positive and can we still simplify this one yep we can still simplify this one to power of 3 it means that you multiply this two by itself three times so 2 power 3 it means 2 * 2 * 2 it's not 2 * 3 it means 2 * 2 * 2 and 2 * 2 * 2 that is 8 so the final answer is 1/ 8 so that's the thing there class if you have a negative exponent you get the reciprocal okay so you pause the video I'll be erasing this example but do not be worried we will have more examples class so we will have eight examples for negative exponents all right now next question sir what if the negative exponent is on denominator okay what if the if you have a negative exponent that would be on denominator so the thing that we will do is we will just put this negative exponent on the numerator and the exponent will be positive so that's the thing there so example if you have 1 /x ra^ of -5 to make this one into positive because we're not allowed class to have a negative exponent it should be positive exponent class okay it should be a positive exponent so if you have a negative negative exponent on denominator the thing that we will do is we will just put it on the numerator to make this one positive okay just put this one on the numerator and this exponent will be positive that would be X raised to the power of 5 and that's it CL that's the answer there example you have 1 over 3 ra to^ of -2 so since we have a negative exponent on denominator just put it on the numerator and the exponent will be positive so that would be so you still have one okay you still have one so copy one then you put this 3^ of -2 on the top so this will be times so since you put this on the top it should be multiplication 1 * this equation 1 * 3 power of 2 so make this exponent into positive so 1 * this equation simply copy 3 power any number multiplied by one the answer is the equation or the number itself so 1 * 3^ two that would be 3^ two and 3 power of two it means you multiply this equation by itself twice so 3 power 2 it means 3 * 3 so 3 * 3 that is 9 so that's the answer there so the thing that we will do class that you need to remember in negative exponent if you have a negative exponent on the numerator put it on denominator and the exponent will be positive now if you have a negative exponent on the denominator put it on the numerator and the exponent will be positive I hope you understand this one class that's the negative exponent class that's the thing there so I hope it's clear for you but do not be worried we will give more examples so let's try number one what if we have X raised the power of -4 what's the answer class that's correct since we have a negative exponent on the numerator we put it on denominator and the exponent will be positive so you put it on denominator that would be x^ 4 of course there should be one here because understood that there's one you get the reciprocal that would be 1 / x ra^ 4 that's the answer class for number one easier right for number one so let's TR TR number two what if we have 2 ra power of -3 what's the answer class so 2 ra power of 3 now since we have a negative exponent on the numerator we put it on denominator class so that exponent will be positive so that would be two power of T and do not forget one class because there is a denominator of one here get the reciprocal that would be 1 over 2 power 3 put it on denominator and the exponent will be positive so this will be 1/ 2^ 3 it means you multiply this two by itself three times this is equivalent to 2 * 2 * 2 and 2 * 2 * 2 that is 8 that's it plus 1/ 8 easy right so let's try number three what if we have 1/ 3 to power of -3 now since our negative exponent is on denominator we put it on the numerator class so since we still have one okay we still have one so copy one multiplied by you put it on denominator numerator since this is -3 on denominator we have 3 part of -3 put it on the numerator to make this one into positive so copy one multiplied by so you put it on the numerator that would be 3 to power of 3 all right so this will be so you can erase this one because we put it on the on the top so this will be 1 * this one so any number multiplied by one the answer is this number itself so copy 3 power 3 and what would be 3 power of 3 class 3 power of 3 it means 3 * 3 * 3 so 3 * 3 * 3 that is 27 all right that's it class that's the answer for number three so let's try number four so number four so we put it here let's put it here Number Four 3 power of x i no 3x ra power of -5 then y ra to power of -4 all right so what what would be the answer class that's correct so let me explain this one now our three here the exponent is one so understood that exponent of three here is one so nothing to do with three simply copy three three will will be still on the numerator copy three now we have X raised to the power of5 since this is5 we put it on denominator okay we have x^ of5 put it on denominator that would be x ra^ 5 now we have y power4 to make this one into positive we put it on the numerator so put it on the top that would be y power 4 that's it class that's the answer for number four EAS right for number four so I hope you're still with me with me with negative exponent so let's try let's try two examples let's try last two examples so pause the video I'll be erasing this one or let's try three examples guys three examples so what if we have okay -5 x ra^ -4 y^ 5 all right all right so what would be our answer class so once again there are so many students they will be confused with this one since we have a negative number now if you have a negative number class do not be worried you need to check the exponent class once again if you have a negative number do not think it this way since this is negative you put it on the denominator so once again there are some students they think it this way if they have a negative number they put it on the denominator directly no it's not okay that's not the answer you always check the exponent once again you will always check the exponent if the exponent is negative and it's on the numerator you put it on denominator if the exponent is negative on the denominator you put it on the numerator but since this NE 5 class the exponent is positive class this NE 5 this is just S Class the the value of five is negative but the exponent class is positive one always remember this one class be careful with this one this5 the exponent is positive one the sign is just negative okay the exponent is positive one so nothing to do with5 -5 is still on the numerator I hope you're not confused with that one class so5 is still on the numerator because the exponent is one we only transfer class if the exponent is negative now since we have a -4 exponent so we put it on the denominator so X will be on the denominator X rais of four and for y the exponent of Y is positive 5 so y still be on the numerator nothing to do with Y class simply copy that's it class that's the answer for number five let's try number six okay last two examples 2^ -3 * 3^ -2 all right what's the answer class that's correct so we need to make this one since this is negative we put it on the denominator so understood that there's one here so that would be one over 2 power of 3 multiplied by so this is negative exponent we put it on the denominator so there would be one understood that there's one here 1 over 3 power of 2 and this will be 1 over 2 power of 3 class what's the answer so once again this is multiplication class because we have a quantity so this equation multiplied by this equation now since we have a negative exponent we put it on the denominator and understood that there's one here on the denominator we need to flip class make this one will be your numerator and this equation will be on the denominator so 2 power 3 it means 2 * 2 * 2 so 2 power 3 that is 2 * 2 * 2 and 2 * 2 * 2 that is 8 so this is 1/8 multiplied by 3 2 it means 3 * 3 it's not 3 * 2 it means 3 * 3 that would be 1 / 3 * 3 that is 9 equals so the final answer will be so 1 * 1 that is 1 8 * 9 that is 72 so multiplying fractions class multiply the numerator 1 * 1 is 1 then multiply the denominator 8 * 9 that is 72 that's it class that's the answer for number six all right so let's try last example then we will be proceeding to the rational exponents last one the rational exponents but we will try last example so what if we have 2^ of -3 I know not not this one 15 over 3 x^ -4 X2 y^ of 3 then y is^ -5 so what would be the answer class so first thing to do you check the number class can we divide 15 by 3 can we divide class 15 by 3 yep we can divide 15 by 3 15 / by 3 that is five so 15 ID 3 that is 5 so five will be on the numerator 15 ID by 3 that is 5 now next since we have a negative exponent for x rais to the power of neg we have X rais the power of negative four so therefore since this is on the numerator we put it on the denominator to make this one into positive so X squ is still positive so simply copy X squ class nothing to do with x squ copy x s x squ will be on the denominator since this is positive okay we only transfer class if the exponent is negative now since this is positive nothing to do with X squ class simply copy x squ x squ will will be still on the denominator class now since we have x ra^ -4 this is negative we put it on the denominator and it will be positive so this will be X ra the^ 4 now since we have a variable close to each other it means multiplication class so we put it on the bottom part so this will be x^ pos4 now since we have x^2 here first so therefore we need to multiply this equation so once again if you have variable close to each other it means multiplication so y Cube copy so y CU is still on the numerator because this is positive then this Y is power of -5 we put it on the numerator and this is negative it will be positive so Y is power of 5 of course this will be multiplication because we have two variables close to each other so that would be five then if you're multiplying class the product rule if they have the same base same y copy y then you will add exponent 3 + 5 so that would be eight and this one same base x copy the base then you will add the exponent product rule class x^2 * x^ 4 same base copy X then you add exponent so I'm sure you know this one class because before going to zero negative and rational exponents you need to master the loss of exponents so 2 + 4 that is x rais the^ 6 that's it class this is the answer for this example all right so you try to answer this one class this will be example number eight so you try to answer this one and you put your answer on the comment section down below just try this one class 5 over 2 ra to power of -3 so you try this one and you put your answer in the comment section down below let me check if you really and really understand this negative exponent rule all right so let's try last one class the Russ rational exponent rule so rational exponent rule all right so you let's try this one so let me erase this one class I hope you understand this negative exponents so you try to answer this one class number eight example so we're done with negative exponents so we will be dealing with rational exponents so rational exponents a ra to power of p/ Q so if you're dealing with rational exponents class it means that you're dealing with fractions exponents of fractions okay fractional exponents class so let's try an example class if you have a part of PQ then quantity ra to the part of M so therefore you need to multiply the exponent so that would be a to the power of P BQ * m okay so once again the exponents are fractions so let's try an example class for you to understand this one so what if we have 3 ra to power of 1/2 * 6 so 3^ 1/2 * 6 so this will be example number one so the thing that we will do is we just simply multiply this exponents so that would be 3 ra the^ of2 * 6 so 1/2 * 6 class what's the answer SO2 * 6 so that would be 1 * 6 that understood that there's one here 1 * 6 is 6 2 * 1 is 2 can we divide 6 by 2 yep 6 / by 2 that is 3 so therefore this is 3 raed to power of two so what would be 3 ra to power of two class that's correct 3 is part of two it means 3 * 3 it's not 3 * 2 class it means 3 * 3 and 3 * 3 that is nine so that's it class that's the answer for number one so just simply multiply the exponents class the fraction and this exponent outside so once again 12 * 6 there are some students class that they can just simply cancel this out because we can divide 6 by 2 6 ID by 2 that is 3 or get the common factor Factor class okay the least H the greatest common factor so 6 we can divide this one by two so 6 ID two that is 3 2 ided by 2 ID by 2 that is 1 and then 1 * 3 that is 3 understood that there's one here 1 * 1 instead of two it it becomes 1 so 1 * 1 that is 1 3 ID 1 that is 3 so same answer CU it depends on you which do you prefer all right let's try another example what if we have have example number two so what if we have five 2/ 3 ultied by 3 okay 5 ra power of 2 over 3 quantity raed to the power of three so how will you answer that one that's correct just simply distribute the exponent or multiply the exponent so that would be 5 ra to^ 2 / 3 * 3 all right just simply multiply the exponent so multiply the exponent plus 2 over 3 * 3 so understood that any whole number whole number three there is an expon a denominator of one so 2 * 3 that is 6 3 * 1 that is 3 can we divide 6 / 3 yep 6 ID 3 that is 2 so therefore okay therefore this will be equal to 5 ra to the^ of 2 so 2 over 3 ultied by 3 the answer is 6 over 3 divide 6 over 3 you can divide the answer is two so 5 squar now what is 5 squ CL 5 squ it means 5 * 5 it doesn't mean 5 * 2 class it means you multiply this five by itself twice 5 * 5 that is 25 that's it that's the answer for number two so let's try number three so number three so we have 2 ra^ 6 x ra^ of 8 y ra to power 4 quantity ra to power 1/2 so what would be the thing that you will do class so rais to power of 1/2 once again this answer is 25 so once again just simply distribute plus distribute the exponent all right so this will be 2 ra to the power of so 6 * 1/2 that would be 6 * 12 then copy X ra to^ of 8 distribute the exponent * 12 then y^ 4 * 1/2 and our answer will be so 6 * 1/2 so 6 * 12 this will be 6 * 1 is 6 then understood that there's 1 here 1 * 2 is 2 6 / 2 that is 3 so this will be 2 ra to power of 3 so we have 2 to power of 3 then 8 * 1/2 so 8 * 12 so understood that there's one here 8 * 1 is 8 1 * 2 is 2 8 ID 2 that is 4 so that would be X ra to the^ 4 then y 4 * 1/2 so 4 4 * 12 understood that there's one here 4 * 1 is 4 1 * 2 is 2 4 / 2 that is two so y power of two and then can we still simplify class this one 2 power of 3 yep we can still simplify this one 2 power 3 it means 2 * 2 * 2 so 2 * 2 * 2 that is 8 so copy 8 then X ra power 4 y to power two that's it CL that's the answer for this example number three all right so easy right so I hope you learned something new today class for this one so let me give you an example class and you put your answer in the comment section down below let me check if you really understand if you really understand the topic class so what if we have so example number four class you try this one class and you put your answer in the comment section down below what if we have 2 ra to^ 4 over 3 ra to the power of 4 then quanti parentheses x ra power of 10 y power of 8 Z ra power 6 ra to the power of 1/2 you try this one class and you put your answer in the comment section down below so you try this one number four and you put your answer in the comment section down below so once again class if you have some questions class with zero negative and rational exponents feel free to leave a comment in the comment section down below class in our YouTube channel you can also message me class in our Facebook Channel same name with our YouTube channel you can always ask questions class with regards to mathematics so I hope you learned something you today and if you like this video do not forget to like share and subscribe you share to your friends and your classmates so that we can help more students especially for those students who are really struggling in mathematics once again this is teacher MJ you have a great day class goodbye for now bye-bye