# How do you simplify  (-2x^2y)^3(5xy^3)^2?

Dec 1, 2017

$- 200 {x}^{8} {y}^{9}$

#### Explanation:

${\left(- 2 {x}^{2} y\right)}^{\textcolor{red}{3}} {\left(5 x {y}^{3}\right)}^{\textcolor{b l u e}{2}}$

First, use the exponent rule ${\left({x}^{a}\right)}^{b} = {x}^{a b}$

$\left({\left(- 2\right)}^{\textcolor{red}{3}} {x}^{2 \cdot \textcolor{red}{3}} {y}^{1 \cdot \textcolor{red}{3}}\right) \left({5}^{\textcolor{b l u e}{2}} {x}^{1 \cdot \textcolor{b l u e}{2}} {y}^{3 \cdot \textcolor{b l u e}{2}}\right)$

Simplify.

$\left(- 8 {x}^{6} {y}^{3}\right) \left(25 {x}^{2} {y}^{6}\right)$

Multiply the coefficients $- 8$ and $25$

$- 200 \left({x}^{\textcolor{red}{6}} {y}^{\textcolor{b l u e}{3}}\right) \left({x}^{\textcolor{red}{2}} {y}^{\textcolor{b l u e}{6}}\right)$

Next, use the exponent rule ${x}^{a} \cdot {x}^{b} = {x}^{a b}$

$- 200 {x}^{\left(\textcolor{red}{6 + 2}\right)} {y}^{\left(\textcolor{b l u e}{3 + 6}\right)}$

$- 200 {x}^{8} {y}^{9}$