[Video] Q13: If a^-1/2 = x, where a > 0, what is a in terms of x ?

Explanation for Question 13 From the Math (Calc) Section on the Official Sat Practice Test 8

So question 13 gives us this equation, 2 right? We have a, to the negative one half is equal to X and 3 they tell us that a is greater than zero. 4 And we want to know what is a, in terms of X, 5 essentially this part of the equation just means solve for 6 a generally speaking, whenever you see the, 7 in terms of part of the question and the sat, 8 that's usually not as important. The important part is the, 9 what is a, so if this, in terms of phrase was something that was 10 throwing you off, just know that what they want you to do is solve 11 for a right. And so we have a, 12 an a is race, the negative one half. 13 And so what we can think about doing right is getting rid of this 14 negative one half X exponent. And one way to do that is 15 to raise this exponent to the negative two, 16 because if I raise it to the negative two, then we might remember from 17 exponent rules, the exponent that are in parentheses 18 to each other, get multiplied together. 19 Now, if I multiply our exponent here, which were negative one half times, 20 negative two, the negatives cancel the twos, 21 cancel, and I get one. So I've now manipulated it so that I have 22 a, to the one is equal to X to the negative two. 23 And so that's the goal because if I'm solving for a, 24 I need a, to have an exponent of negative of positive one. 25 And so my whole goal here was to eliminate this negative one half exponent, 26 and now I have excellent negative two, and this is right. 27 There's nothing wrong wi...