# How do you simplify (- 1/5)^-2 + (-2)^-2?

Jun 6, 2016

$\frac{1}{- \frac{1}{5}} ^ 2 + \frac{1}{- 2} ^ 2 = 25 \frac{1}{4}$

#### Explanation:

As ${a}^{- n} = \frac{1}{a} ^ n$, ${\left(- \frac{1}{5}\right)}^{- 2} + {\left(- 2\right)}^{- 2}$ can be written as

$\frac{1}{- \frac{1}{5}} ^ 2 + \frac{1}{- 2} ^ 2$

= $\frac{1}{{\left(- 1\right)}^{2} / {\left(5\right)}^{2}} + \frac{1}{4}$

= $\frac{1}{\frac{1}{25}} + \frac{1}{4}$

= $1 \times \frac{25}{1} + \frac{1}{4}$

= $25 \frac{1}{4}$