Explanation for Question 11 From the Math (No Calc) Section on the Official Sat Practice Test 7
Question 11 asks the expression X to the negative two times Y 2 to the one half over X to the one-third times Y to the negative 3 first where X is greater than one and a white is greater than one 4 is equivalent to which of the following. So the first thing I'm going to 5 do is just rewrite this, but by separating the terms, 6 just so that I can see what they look like separate. So X to 7 the negative two over one times Y to the one half over one times, 8 one over X, the one third times one over Y 9 to the negative one. So the rules we're going to need here, 10 or there are two rules that we're going to need here. First, 11 a term to a negative power is just the reciprocal of what it's originally 12 written as. So for example, if you have X to the negative third, 13 that's just the equivalent of one over X to the third. 14 So if the term is in the denominator, 15 you put it in the new grader. And if it's in the numerator, 16 you put it in the denominator. The second role is about fractional exponents. 17 So if you have a term to a fractional exponent, 18 let's say excellent, one half, that's just equal to, 19 uh, the root of that term to the denominators power. 20 Uh, and then the term inside that root is to the numerators power. 21 So this is just equal to root X. 22 So knowing those rules, I'm going to rewrite these terms we have at the 23 top. So starting with, 24 uh, X the negative two, well, that's just equal to one over X squared. 25 Y to the one half is just equal to root Y X 26 to the one. Third is just equal to one over X, 27 the cute root. And finally Y to the negative one is just 28 equal to Y. Now we can rewrite this, 29 uh, as Y times root Y over X 30 squared times root three X, 31 and that's actually answer choice D so we know that that's the.