# How do you simplify (r^-2)^4 and write it using only positive exponents?

Sep 3, 2016

${\left({r}^{- 2}\right)}^{4} = \frac{1}{r} ^ 8$

#### Explanation:

We can write ${a}^{- m} = \frac{1}{a} ^ m$, as a^(-m)×a^m=a^(-m+m)=a^0=1 and hence ${a}^{- m} = \frac{1}{a} ^ m$.

Therefore ${\left({r}^{- 2}\right)}^{4}$

= r^(-2×4)

= ${r}^{- 8}$

= $\frac{1}{r} ^ 8$