# How do you simplify -5^-2?

Mar 10, 2016

$\textcolor{b l u e}{- \frac{1}{25} \mathmr{and} - 0.04}$

#### Explanation:

$- {5}^{-} 2$

since, ${x}^{-} 1 = \frac{1}{x}$,

therefore,

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

= 1/(-(5)(5)

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

If the negative was meant to be part of the power, one would need to write ${\left(- 5\right)}^{-} 2$

Mar 10, 2016

$- 0.04$

#### Explanation:

$- {5}^{-} 2$

Remember ${a}^{-} n = \frac{1}{{a}^{n}}$

and that $- a = \left(- 1\right) \cdot a$

since the order of operations has us do powers before multiplication, the power does not affect the $- 1$. The other way to look at it is that the power ${5}^{-} 2$ is being subtracted, in which case the order of operations also tells us to do the power before the subtraction:

$\therefore - {5}^{-} 2 = \left(- 1\right) \cdot \frac{1}{5} ^ 2$

$= - \frac{1}{\left(5\right) \left(5\right)}$

$= - \frac{1}{25} = 0.04$

If the negative was meant to be included in the power, it would need to be written as ${\left(- 5\right)}^{-} 2$