# How do you simplify (-2r^(-4))^(2)(-3r^(2)2^(8))^(-1) ?

May 7, 2018

$- \frac{1}{172 {r}^{10}}$

#### Explanation:

There are two laws of indices which we can use to start.

#(xyz)^color(blue)(m) = x^color(blue)(m)y^color(blue)(m)z^color(blue)(m)" and " x^color(red)(-m) = 1/x^color(red)

${\left(- 2 {r}^{- 4}\right)}^{\textcolor{b l u e}{2}} {\left(- 3 {r}^{2} {2}^{8}\right)}^{\textcolor{red}{- 1}}$

$= {\left(- 2\right)}^{2} {r}^{- 8} \times \frac{1}{- 3 {r}^{2} {2}^{8}} ^ \textcolor{red}{1}$

$= \frac{4}{\textcolor{t e a l}{{r}^{8}}} \times \frac{1}{- 3 \textcolor{t e a l}{{r}^{2}} {2}^{8}} \text{ } \leftarrow \textcolor{t e a l}{{x}^{m} \times {x}^{n} = {x}^{m + n}}$

$= - {\cancel{4}}^{1} / \left(3 \textcolor{t e a l}{{r}^{10}} {\cancel{256}}_{64}\right)$

$= - \frac{1}{172 {r}^{10}}$