In Exercises 101–108, simplify by reducing the index of the radic...

Question

In Exercises 101–108, simplify by reducing the index of the radical. ⁹√x^6 y^3

Accepted Answer

Welcome back. I'm so glad you're here. We've got an expression here. We've got the 12th root being taken of A. To the ninth, B. To the eighth. And where to simplify. Well, we can't take anything out from the radical because there aren't 12 of anything. But we do know another way to write this. We know that this index of a radical is the same as being the denominator of an exponent, so instead of A. To the ninth in here it's A. To the 9/12. And for B that eight is in the numerator and the 12 is in the denominator. So be to the 8 12. We can reduce those fractions. A. to the 9/12 becomes a. To the 3/4, And B to the 8/12 becomes b to the 2/3. We look at our answer choices in this matches with answer choice. A while done, we'll catch on the next one.

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