Explanation for Question 12 From the Math (Calc) Section on the 2017 May Sat
Progression. Well, they just want us to say what expression or what answer choice 2 is the same as the one they give us here. 3 Um, so essentially we're just simplifying whenever we want. 4 We have, uh, exponents on the outside of parentheses. 5 We know we have to distribute that to every term. 6 So to do that, we're going to have 16 to the one, 7 half X to the nine to the one, 8 half and Y to the third, 9 to the one half. Now, 10 if you're a member having a one half exponent 11 is the same thing as taking the square root of something. 12 So for example, if we have X to the one half, 13 that's the same as the square root of X when we do have, 14 um, oh, I don't know if you all saw that. 15 Let me repeat that. So when we have X, 16 the one half, that's the same thing as saying the square root of X. 17 When you do have, um, an just any fraction as an exponent, 18 we can call that X to the, 19 a over B. And the rule is that B is your 20 index for your root and a stays as the 21 exponents. So the numerator is still the exponent. 22 The denominator goes on the index for the root. 23 In the case of one half, the index is two. 24 So it's the square root, but that could be any number in this case. 25 We're just going to look at the one half. So let's say the 16 26 to the one half we said, that's like the square root. 27 So we have the square root of 16 times. 28 Now we have something a little different here because we still have the X 29 to the night, but we're just taking the square...