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Exponent Properties 3. Created by Sal Khan and Monterey Institute for Technology and Education.
Video transcript
Simplify x to the third, and then that raised to the 4th power times x squared, and then that raised to the 5th power Here we'll 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 bth power, this is the same as x to the a times b power. To see why that works, let's try that with the - well I won't do that with these right here - I'll do it with a simpler example. let's say we are taking x squared and 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 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 ... like, I have the same base, I'm taking the product ... so I can just add the exponents. So this is going to be equal to - let me do it in that same magenta - x to the two plus two plus two power ... or essentially x to the three times two. This right here is just 3 times 2, So we get x to the 6th power. So you say "hey sal, I don't see why you can add those exponents..." Well, this over here we can write as x times x, times x times x, -- In parentheses I'm putting each of these x squareds.-- times x times x. And this is just x times itself 6 times, or x to the 6th power. This is why we can add the exponents like that. So let's use this powers of exponents property on this expression right over here. To start off we have x to the third raised to the fourth power. So that's just going to be x to the three times 4 power. or x to the 12th power. Then we muliply that by x squared raised to the fifth power well that's just going to be x to the 2 times 5 power, or x to the tenth power. And now that we have the same base, and we're taking the product, we can just add the exponents This is going to be equal to - this whole expression is going to be equal to x to the 12 plus 10th power, or x to the 22nd power. And we are done!