In Exercises 91–100, simplify using properties of exponents. (x^2...

Question

In Exercises 91–100, simplify using properties of exponents. (x^2/3)^3

Accepted Answer

Hello. Today we're going to be simplifying an exponential value. So the given exponential value is be raised to the fourth power. All of that raised to the power of 1/8. Now, in order to continue this problem, let's go ahead and recall our exponential multiplication are exponential multiplication states that if we have a value of X raised to the power And that value itself is raised to the 8th power, all you're going to do is multiply the powers together. So this will give us X to the power of end times a. Now we're gonna go ahead and apply that rule right here in order to reduce the exponents, multiplying both of the exponents together is going to give me b. Race the power of four times 1/8. Now multiplying four and 1/8 together is going to give me be raised to the power of 4/8. Now 4/8 can be reduced. The numerator and denominator is divisible by four and that's going to be be raised to the power of a half. Now we could rewrite this 11 more way. Recall that X. Race the power of a half is the same thing as the square root of X. So rewriting our B term into the square root is going to give me the square root of B. And that means our solution to this problem is going to be C. So I hope this helps you apply the exponential multiplication rule to simplify exponents and I'll see you all in the next video

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