In Exercises 91–100, simplify using properties of exponents. (20x...

Question

In Exercises 91–100, simplify using properties of exponents. (20x^1/2)/(5x^1/4)

Accepted Answer

Welcome back. I'm so glad you're here. We are simplifying this expression, we've got two terms that are being multiplied. We can start off with the coefficients. We've got six times three. Yeah, that's 18. And yeah, our answer choices are 18. So yeah, we did that right. And now we've got the tricky part, we've got the white of the 4/5 and we've got the y to the nine over to the nine seconds and we've got two exponents that are being multiplied. We are going to add them together. So what we're going to add 4/5 plus nine seconds. And in order to add two fractions, we've got to have a common denominator. Common denominator between five and two is 10. We look at each of those and we say how do we get from 5 to 10? We've got to multiply it by two. Do the same to the top and the bottom. So in effect we're multiplying it by one, we look at to how do we get from 2 to 10? We multiply by five. What we do to the bottom. We've got to do that. The top. So that in effect we're multiplying it by one. We'll go ahead and do that multiplication and we'll get 8/10 plus 45/10, combining those enumerators, we get 53 the denominator stays and that is as simplified as that one is going to get. So we've got 18 Y to the 53/10. That's as simplified as we can do. We look at the answer choices and that is answer choice. A well done, we'll catch you on the next one.