# How do you simplify -5^-3?

Oct 29, 2015

$- {5}^{-} 3 = - \frac{1}{125}$

#### Explanation:

In the expression $- {5}^{-} 3$ there are 2 operations: power and multiplication by $\left(- 1\right)$. According to the order of operations we have to calculate the power first remembering, that if the exponent is negative we have to write the expression as a positive power of the reciprocal of the base:

${\left(\frac{a}{b}\right)}^{-} c = {\left(\frac{b}{a}\right)}^{c}$

So we get: $\left[- \left(\frac{1}{5} ^ 3\right)\right]$
Finally we can calculate the power ${5}^{3}$ and write the final answer:

$- {5}^{-} 3 = - \left(\frac{1}{5} ^ 3\right) = - \frac{1}{125}$