# How do you simplify (-5)^-2?

Apr 5, 2018

It simplifies to $\frac{1}{25}$ or $0.04$.

#### Explanation:

Use the definition of a negative exponent:

${x}^{\textcolor{b l u e}{- m}} = \frac{1}{x} ^ \textcolor{b l u e}{m}$

Here's the expression:

$\textcolor{w h i t e}{=} {\left(- 5\right)}^{\textcolor{b l u e}{- 2}}$

$= \frac{1}{- 5} ^ \textcolor{b l u e}{2}$

$= \frac{1}{- 5 \cdot - 5}$

$= \frac{1}{\textcolor{red}{\cancel{\textcolor{b l a c k}{-}}} 5 \cdot \textcolor{red}{\cancel{\textcolor{b l a c k}{-}}} 5}$

$= \frac{1}{5 \cdot 5}$

$= \frac{1}{25}$