# Negative Exponents

In this video, we are going to look at how to simplify numbers raised to negative exponents.
For example:
To simplify the following:
$4^{-2}$
we have to move the 4 to the denominator, and make the exponent positive.
$\frac{1}{4^2}$
Then, multiply the 4 by itself, 2 times which would simplify to:
$4 \times 4=16$
$\frac{1}{16}$
To simplify the following:
$x^{-3}$
we have to move the x to the denominator, and make the exponent positive.
$\frac{1}{x^3}$
If there is something more complex such as $5x^{-2}$ then only the x will go to the denominator since it is the one with the negative exponent. This will be simplified to
$\frac{5}{x^2}$

Other examples:

$x^{-b}= \frac{1}{x^b}$
$8^{-3}= \frac{1}{8^3}$

• ## Want full access to all of our free math tutorials & practice problems?

Used by students across the country. Pre-Algebra, Algebra I, Geometry, & Algebra II