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# Exponent properties 3

## Video transcript

simplify X to the third and then that raised to the fourth power times x squared and then that raised to the fifth power now here we're going to use the power property of exponents sometimes called the power rule and that just tells us if I have X to the a and then I raise that to the B power this is the same thing as X to the a times B power and to see why that works let's try that with a well I won't do it with these right here I'll do it with a simpler example let's say we are taking x squared and then raising that to the third power well in that situation that literally means multiplying x squared by itself three times so that literally means x squared times x squared times x squared I'm taking x squared and I'm raising it to the third power now what does this mean over here well there's a couple of ways to do it you could just say look like I have the same base I'm taking the product I can just add the exponents so this is going to be this is going to be equal to let me do it in that same magenta this is equal to X to the 2 plus 2 plus 2 power or essentially X to the 3 times 2 this right here is just 3 times 2 so we get X to the sixth power and if you want you say hey Sal well I don't understand why you can add those exponents you just have to remember that x squared this thing right over here we can rewrite as x times X times X times X and parentheses I'm putting each of these X Squared's times X times X and this is just x times itself 6 times x times X times X times X times X times X this is just X to the sixth power so that's why we can add the exponents like that so let's just use that power property on this expression right over here we start off with we have X to the third raised to the fourth power so that's just going to be X to the 3 times 4 power or X to the twelfth power then we're multiplying that by x squared raised to the fifth power well that's just going to be X to the 2 times five power or X to the tenth power and now we have the same base we can and we're taking the product we can just add the exponents this is going to be equal to this whole expression is we're going to be equal to X to the 12 plus tenth power or X to the 22nd power and we are done