# How do you simplify (-kv)^2(-kv)^3(-kv)^4?

Sep 29, 2015

$- {k}^{9} {v}^{9}$

#### Explanation:

$\textcolor{red}{{\left(- k v\right)}^{2}} \textcolor{b l u e}{{\left(- k v\right)}^{3}} \textcolor{g r e e n}{{\left(- k v\right)}^{4}}$

$\textcolor{w h i t e}{\text{XXX}} = \textcolor{red}{{\left(- 1\right)}^{2} {k}^{2} {v}^{2}} \cdot \textcolor{b l u e}{{\left(- 1\right)}^{3} {k}^{3} {v}^{3}} \cdot \textcolor{g r e e n}{{\left(- 1\right)}^{4} {k}^{4} {v}^{4}}$

$\textcolor{w h i t e}{\text{XXX}} = \left(\textcolor{red}{{\left(- 1\right)}^{2}} \cdot \textcolor{b l u e}{{\left(- 1\right)}^{3}} \cdot \textcolor{g r e e n}{{\left(- 1\right)}^{4}}\right) \cdot \left(\textcolor{red}{{k}^{2}} \cdot \textcolor{b l u e}{{k}^{3}} \cdot \textcolor{g r e e n}{{k}^{4}}\right) \cdot \left(\textcolor{red}{{v}^{2}} \cdot \textcolor{b l u e}{{v}^{3}} \cdot \textcolor{g r e e n}{{v}^{4}}\right)$

$\textcolor{w h i t e}{\text{XXX}} = {\left(- 1\right)}^{9} \cdot {k}^{9} \cdot {v}^{9}$

$\textcolor{w h i t e}{\text{XXX}} = - {k}^{9} {v}^{9}$