# Thread: How to Solve this type of problem for practice SAT?

1. ## How to Solve this type of problem for practice SAT?

Hello members,

I am working on my SAT practice and i came across this problem.

$x^-2=16$

I dont remember learning this. Any help would be appreciated. Thanks.

PS. That is supposed to be X to the -2 power.

2. This equation is the same as

$\dfrac{1}{x^{2}}=16.$

You can flip both sides to obtain

$x^{2}=\dfrac{1}{16}.$

Does that give you any ideas?

3. Yes, Thank you for the help!

4. $\displaystyle \frac{1}{x^{2}}=16 \implies 1 = 16x^2 \implies \dfrac{1}{16}=x^2 \implies x = \sqrt{\frac{1}{16}}$

5. Originally Posted by pickslides
$\displaystyle \frac{1}{x^{2}}=16 \implies 1 = 16x^2 \implies \dfrac{1}{16}=x^2 \implies x = \sqrt{\frac{1}{16}}$
$\displaystyle x = \mathbf{\pm}\sqrt{\frac{1}{16}}$

6. Here is a quick way to get the answer on the SAT:

$x^{-2}=16$

Simply raise both sides to the reciprocal power:

$(x^{-2})^{-\frac{1}{2}}=16^{-\frac{1}{2}}=.25$

So grid in $.25$

Notes:

(1) To solve this you only need to type the following into your calculator: $16^{-.5}$

(2) If this were a multiple choice question you could simply plug the answer choices in for x in the original question. You should almost always start with choice (C) when using this strategy. (Of course the solution I have given is better, but it requires some mathematical knowledge, whereas this one does not.)

(3) Note that this problem is incomplete as you have stated it since -.25 is also a solution. So either you haven't written the question precisely or this isn't an actual SAT practice problem. In any case, the solution to a grid-in can't be negative.

(4) The above posters have given a better solution to this problem, but on the SAT you don't generally want the most complete solution. You want to get the answer as quickly and efficiently as possible.