[Music] Hello everyone is welcome to this mini recovery on the laws of exponents. The laws of exponents are seen together at 3 but are also reusable. The map is in 2D as a whole. Today we see the powers of certain names, then we see the changes of bowles, then we will see the laws of exponents and we will finish with some examples. So here we go. We had some vocabulary words to define to fully understand this mini recovery. So we discuss exponents and power, and here in my example the 5 represents the base, the 3 represents the exponent, and the 125 is the result of my board assigning an exponent that gives me my power. It is also important to be more than five exponents. 3 does not equal 5 x 3, but indeed 5.535. When we have a positive exponent, in Nantes, we ask ourselves what is more precise? The exponent represents the number of times a man is multiplied by the human being. In the negative and fractional exponents, that will be different but we will talk a little bit later in the videos when we do exercises with exponents it is interesting to know certain powers in fact the powers we are interested in are the powers of prime numbers like and power of 2.3 2.5 service of 11 of janeiro so powerful which will interest us this sealed power of 10 powers which come back in many exercises in fact here what will be interesting to know for example 243.7 a power of 3 if you know that in addition too many exponents 5 gives 243 is even easier in these exercises but it is not obligatory to connect by case to properly apply the laws of exponents you must be able to make changes first before anything a question for you true or false eloi the exponents are well applied in this calculation I in fact here we realize and the laws of exponents are not well applied in this calculation is the error was made from the beginning so we did not have the same base and that we are prepared for the subtraction of our exponents the correct approach for this calculation is as follows so we change our base cie or twice 3 and after its epic our laws of exponents to complete the problem here is an example of changing banks in crisis and we had two exponents 4.60 case we realize that these are 4 not the same base as my other land so I changed to 64 to have the same match not bondy exponents 4 it does not change and that I have always exposed in four and we realize that 64 is a power of 2 gives two exponents sepsi then I am not used to the laws of exponents now that I have the same board so can add the exponents to obtain two exponents from here we are now out of water at the heart of the subject of this mini recovery is the laws of exponents before anything else we must make a few small reminders so we know that we have a variable or a number with an exponent 0 that gives us a in fact we will realize that the laws of exponents apply whether they are names or whether they are varia when an exponent 1 we just do we actually we are the skin cries but it is important not to forget that we have an exponent a year our calculations with even if I have a goal here with no exponent we must remember that these oxen exponents 1 we must also will be more than to vote the laws of exponents we need the same base everywhere in our calculations here is the first law of exposition so it is the product of power when I multiply two terms with an exponent which have the soul embers I add the exponents so here an example I have this exposition in three months this exponent eight times seven exponents - k so my base is the same everywhere that it generates and that j 7 and a single johnson the exponents I have three the one which gives 11 and I do to the plus -4 so even if a negative number to audition it 11 plus -4 it gives me it is I have seven exponents It's a funny coincidence that we have a base with a similar exponent, but it happens. We realize here in our second example that I simply changed the base, the exponents are the hands are managed, write my ban ki moon and that same calculation but exposes with troyes more on the this minus 4 gives me 7 I found that she alston less than she the uci is drunk exponents it is here is the next law of exponents which is the power quotient in fact we realize that the law looks a lot like it that we just saw except that this time its a division by a division we must subtract the exposes here are some examples no I have three exponents 9/10 is too exposed in two again we came to rewrite our base it is 3 to make 9 - which it gives me it is it is the same thing for which first etc 6% Monday by sex for two months gives this exponents will now the power of a power made when I have a power between parentheses affected by an exponent I first want to multiply but exponents together here is an example so I have five exponents three exponents 4 all in parentheses exponents 5 and that I will have to multiply all but exponents together 3.4 which gives me dose and 12.5 gives 60 and manage cream base and again 5 and my exposition 1.435 which gives me either that we realize that for the second example I only changed the ball is that I see obtaining from them rosa now the power of a product no because I have a product at foix oxen in parentheses exponents m I distribute my exponents to each of my factors here is an example so I have three times two exponents 5 I will find my 5 to each of my factor is here two young people this tribute to man 3 and I will obtain 3 15 to e exponent st finally the same thing for my example a little more beautiful game my exponents 5 to others but factors eight exponents 5 x exponents 5 and y exponent for the power of a quotient we do the same thing as the power of a product fact that we will distribute our exponents to each of our term in our action so I have to instruments m.hamon numerator and the denominator once again offered an example so 4/9 exponents 3 will become 4 exploding to three aimed by nine exponents 3 it is the same thing for the example so far with variables so I will obtain them exploding to three rockets by f 3 when we have a negative exponent or they become positive we must reverse its position so for example young negative exponents in the numerator game to see the master in the denominator obtained in positive exponent same thing I have negative exponent in the denominator on the kingdom numerator or have an exponent also offered some examples years so if I have eleven exponents -3 and I will have a positive exponent I want first reverse its position with the denominator to get one this eleven exponents to 3 they damascus thing that we have variables and that I exposed in minus 3 and that I see it is its position are given one on x exponents 3 when my exposure in negative and to the denominator I will have to send it to the numerator is here I will obtain 5 to the 1 2 and if I want to obtain x we are presented again the power of a negative exponent but this time corn hot boys is a traction before anything else I have a question for you among the equalities following which is false I leave a few seconds to think in fact here we realize the equality which reaches and here because I have a negative exponent I must pour the numerator and the denominator but the sign does not change and which if I would have said to have a number or a term in fact also let's talk now about the power of a reactionary exponent but before anything else I have a question for you among the equalities following which is true so I give me a few seconds to think and insults Jonah answer the correct answer this is two so when I have a good affected by a fractional exponent the denominator becomes 'the index of my root and the numerator becomes the exponent of my bank if I have an exponent a half it will be a square root young exponents audience is a cube root and young exponents again it will be maintained 4th et cetera et cetera let's do examples if I have five exponents a third here in the bottom non denominator becomes one 10 my root so I would like it is the cube and my barrows does not change and my operator but it is the exponent of the stock market and this is not necessary wrote the same thing for aix exponents interior we do not change the ball what it will be still a cube root 2 here with them like Mrs. Boyer we do not need to write it other examples when I have five exponents three bodies have denominator becomes one 10 of my roots and I want roots to sort from five exponents to 3 what my numerator it cc3 it becomes the exponent of the stock market good example in bumps it's the same thing except that changes the base so I obtained roots prayer of x 3 here now and laws of exponents so if two powers of the same base are equal then the exponents are equal what that means is that if I have to exponents m is equal to exponents m then my exponents will be equal here is an example excluded four exponents 3d there are four exponents x what that means is that believes equals a so that allows us to solve equations and we will use it later in our exempt here is a first example of application of the laws of exposition if you want to put me on pause the video and sfr the number by falling because I am going to give the approach to instinct so the thing we are going to do we will start when we have the following program at 10 street mount exponents 3 to each of my invoices internally the parenthesis so I will get two exponents three exponents 3 May Swiss exponents then I take care of the multiplication fact that I exposed in three months has exposed in less certainly with three plus -7 that gives me minus 4 I want to exponents - k and finally I finish with the term which is here with -8 b to the 16th by credit card exposed to 1.5 and that I do minus 8 / 4 which gives me minus two b exponents certainly / brawl opposing 5 the that I do certainly minus 5 which gives me my exposure in 2 gb exponents 2 once I have that I distribute world animator to each of my term in the numerator I have the following results and there I will look if I can not simplify terms together in it if we realize that two expose 1.3 on the circuit with the two to obtain from the exponent 2 exploding to three I do not have the computer term with it remains to exponents 3b exponents 6 10th beard exponents 2 that gives me exponents kia and I subtract music to the 1 here to exponents - eighty negative exponents we do not want to expose it negative so I will send it to the denominator and in mathematics we always write the variables in alphabetical order I still have to take care of a mode last fraction with g2b exponents 2,18 by two bugs to the in two and that it is as if I had 5 / 5 that gives a name that is put there term to simplify I obtain a one does not forget either to report the negative sign which was in front of my reaction here is a second example of application of the laws of the exposes so we will start by solving the expression is outside the parenthesis at the level term on the ground so if I have cube root of this exponents 18 years that we remember that a cube root and it is an expose by fractionating and that I was able to expose an eighteenth inning and 18 10 by three which gave these exponents sips then I dress multiplication here with I add the exponents 9 the cert madone 16g exposes in 16es it is a power of a power with three times 5 gives me I will that I try exponents at the stage that I have a division also made that I must substrate but exponents etc 6 - 16 gives me minus 10 and here I have six opponents 15 watts 80 exposes years there is auxi budget a multiplication I must add the exponents and 15 the cert gives me 22 once I am there I must extra the root so I did the root of 81 which gives me nine and we remember that a root because them when we have an exponent it becomes an offense and that these exponents 22 / 2 which will give me its exponents then what I must do is here to the denominator g exposing minus rose and exposing we must add the exponents because jadson the exponents - 11 above it gives me zero as for its exponents 0 we made any number exponents 0 it always gives me one and on what he knows audinet engine I only have 9 in fact I have nine times we were right is what I have to do now is to apply my exposition in half to each of them the terms of my reaction as you see right here these exponents - ten exponents a half I was saying to myself minus 10 with a 2005 give minus five and nine exponents millions this reminder which mixes an exposition by fractioning it is the stable has only yielded to rue root body and 2.9 gives me 3 I now have to get rid of its negatives which is here ex exponents - five games lanvaux denominator so that they become positive I get one out of 3 6% 5 which is my final answer here is a last example of application of the laws of exponents with here we will want to solve the following equation so after as long as we want to make quote to take the if this one and from there components prime factors and that we obtain twice three exponents 3 why do this not what we will see the same base everywhere to be able simple idea term or factors and here eight becomes two exponents 3 and my last term 8 does not change so once I have that I can distribute montroy to all but factor to the interest of my part in mind and I have two exponents with three voices three exponents 3 and here there is nothing that changes on my side of equality we realize that we have two explosions with three on each side of my agent and that I can lead simplify them now that they are simplified I hold the following results here we saw earlier in our hearts particular that when I have a base affected by an exponent excellent same base affected in our texts to the aces the exponents see to be equal so I can just that we were talking but exponents etc 3 is equal to 2 6 months 9 does not solve algebraic part with I did the reverse operation I send my work to the other side in June +9 and insurgents divided by two to find that my six plated my x is equal to these we are finished solving this equation but we can check ourselves with this type of problem so I go back to my initial equation and I come to replace exponents ixe art 6 so the value that I like to find it see if it is indeed the same result on each side of my equality with three exponents 2 x 6 months 9 gives me three exponents 3 wolfsburg 1-3 equals 27 and six exponents 3 216 and I continue my calculation and I finally obtain that 216 is equal to 200 it is that we do not finish our problem and in addition we have verified it is this which puts an end to this mine is recurrent on the laws of exponents the call you who before applying the laws of exponents we must make our basic changes to have the same bases now it remains to settle and exercise them and I put questions you can consult our website in order to become a champion a champion by everyone [Music]