In Exercises 91–100, simplify using properties of exponents. (25x...

Question

In Exercises 91–100, simplify using properties of exponents. (25x^4y^6)^1/2

Accepted Answer

welcome back. I'm so glad you're here. We've got an expression, we have 49 A. To the eighth, B to the 12th and that's all raised to the one half. We are to simplify using the laws of exponents. What I'm going to do first is I'm going to take this one half that all of these terms are being raised too, and I am going to distribute this one half. We recall from previous lessons that when we have an exponent raised to another exponent that we are going to multiply those two exponents together. And for this 49 it's like the 49 is raised to the first, so we're going to take that one times one half. So 49 to the one times one half, or 49 to the one half, It's going to be a raised to the 8th times 1/2 And be raised to the 12th times one half. Now we can go ahead and do that multiplication. So 49 to the one half and a to the eight times one half. Well that's eight of the fourth and B to the 12 times one half. Well that's B to the sixth. And now the only simplification we have left is at 49 to the one half. Well that's the same as the square root of times eight of the fourth to the sixth and the square to 49 is seven, so we have seven A to the fourth, B to the sixth. We look at our answer choices and that matches with answer choice. A. Well done. We'll catch you on the next one.

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