# What is 1/2 to the negative fourth power?

## ${\left(\frac{1}{2}\right)}^{-} 4$

Apr 20, 2018

${2}^{4} = 16$

#### Explanation:

Recall that ${\left(\frac{a}{b}\right)}^{x} = {a}^{x} / {b}^{x}$, so

${\left(\frac{1}{2}\right)}^{-} 4 = {1}^{-} \frac{4}{2} ^ - 4$

${1}^{-} 4 = 1$, as $1$ raised to any power is $1.$

So, we get

$\frac{1}{2} ^ - 4.$ Recall that you can get rid of a negative exponent in the denominator by moving it to the numerator, making it a positive exponent, and vice versa. IE, $\frac{1}{a} ^ - x = {a}^{x}$

So,

$\frac{1}{2} ^ - 4 = {2}^{4} = 16$