# How do you simplify (1/2)^-2?

Apr 17, 2018

$4$

#### Explanation:

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

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

${1}^{-} 2 = 1$ as $1$ raised to any power is just $1.$ So, we have

$\frac{1}{2} ^ - 2$

Recalling that ${a}^{-} x = \frac{1}{a} ^ x ,$ we get

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