In Exercises 85–116, simplify each exponential expression.(x⁻⁵y⁸/...

Question

In Exercises 85–116, simplify each exponential expression.(x⁻⁵y⁸/3)⁻⁴

Accepted Answer

Hello, today we're gonna be simplifying the given expression. So what we are given is A to the power of negative eight times B to the power of 11/5 all race to the power of negative three. Now, in order to simplify this expression, the first thing we're going to do do is distribute the value of negative three to B to the power of 11 A to the power of negative eight and five. And that is going to give us A to the power of negative eight race to the power of negative three times B to the power of 11 race, the power of negative three all over five race to the power of negative three. Now, immediately you can see that we have a bunch of negative exponents that we want to write as positive exponents. If we move the quantities A to the power of negative A and B to the power of to the denominator, we can rewrite these exponents as positive values. And if we move five to the power of negative three to the numerator, we can rewrite it with a positive exponent. So doing this allows us to rewrite the expression as five to the power of positive three over A to the power of negative eight race to the power of positive three times B to the power of 11, raise the power of positive three. So in order to simplify the values in the denominator, we can go ahead and use the property of exponential multiplication. And that states that if you have a to the power of M raise to the power of N, you can simplify the exponents by taking the product of the exponents. And that is going to give us A to the power of M times N. So for a race to the power of -8 race to the power of three, the product of the exponents is going to give us A to the power of -8 times three. And that is going to simplify to give us A to the power of -24. And for B to the power of 11 race to the power of three, the product of the exponents is going to give us B to the power of 11 times three, which is going to simplify to give us B to the power of and five races to the power of three can be rewritten as five times itself three times which is going to simplify to give us 125. So we can rewrite the expression as 125 over a to the power of negative 24 times b to the power of 33. And again, we have a value with the negative exponent in the denominator. So if we move the, a term to the numerator, we can rewrite that term with the positive exponent. And that is going to give us the value of 125 times a to the power of 24 all over B to the power of 33, which is going to be the simplified form of the given expression. And with that being said, the answer to this problem is going to be C so I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

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In Exercises 85–116, simplify each exponential expression.(x⁻⁵y⁸/3)⁻⁴

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