# Exponents

## Mathematics: Exponents

According to the Knowsys Method, the first thing you should do when facing a math problem is to read carefully, then note the bottom line, assess your options, and attack the problem.

If $x^{-2}=16$, what is the value of $x^{2}$?

At the top of your scratch work, write the bottom line.  $x^{2}=?$

In most problems you would want to solve for x, but here you need to solve for $x^{2}$ instead. How do you do that?

First, notice that the given exponent is very similar to what you need to find. To correct negative exponents, convert each term to its reciprocal. Since you do not have a fraction to start with, simply put 1 in the numerator.

$\frac{1}{x^{2}}=16$

To get the variable out of the denominator, multiply both sides by $x^{2}$

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

After canceling out $x^{2}$ on the left-hand side of the equation, you are left with $1=16x^{2}$  Divide both sides by 16 to isolate $x^{2}$

$\frac{1}{16}=\frac{16x^{2}}{16}$

$\frac{1}{16}=x^{2}$

Now loop back to your bottom line and check whether you answered the correct question.

$x^{2}=?$

Look at the answer choices to make a final selection:

$A) \frac{1}{16}$

$B) \frac{1}{4}$

$C) 2$

$D) 4$

$E)12$