How do you use the laws of exponents to simplify the expression (-2x^2y)^3(5xy^3)^2?

May 21, 2018

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

Explanation:

${\left({a}^{b}\right)}^{c} = {a}^{b c}$
$\left({a}^{b}\right) \left({a}^{c}\right) = {a}^{b + c}$
${\left(a b c\right)}^{d} = {a}^{\mathrm{db}} ^ {\mathrm{dc}}^{d}$

So, we have:
${\left(- 2\right)}^{3} {\left({x}^{2}\right)}^{3} {y}^{3} {\left(5\right)}^{2} {x}^{2} {\left({y}^{3}\right)}^{2}$

${\left(- 1\right)}^{3} {\left(2\right)}^{3} {\left({x}^{2}\right)}^{3} {y}^{3} {\left(5\right)}^{2} {x}^{2} {\left({y}^{3}\right)}^{2}$

${\left(- 1\right)}^{3} {\left(2\right)}^{3} {x}^{6} {y}^{3} {\left(5\right)}^{2} {x}^{2} {y}^{6}$

${\left(- 1\right)}^{3} {\left(2\right)}^{3} {x}^{8} {y}^{9} {\left(5\right)}^{2}$

$- 1 \left(8\right) \left(25\right) {x}^{8} {y}^{9}$

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