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

Sep 27, 2016

$81 {x}^{8} {y}^{12}$

#### Explanation:

Recall: two of the laws of indices:

${\left({x}^{p}\right)}^{q} = {x}^{p q} \text{ } \leftarrow$ (multiply the indices)

${\left(x y\right)}^{p} = {x}^{p} {y}^{p} \text{ } \leftarrow$ (each factor is raised to the power)

Apply the laws to each factor separately

(-3x^2y^3)^4 = (-3)^4 xx (x^(2))^4 xx y^3)^4

=$+ 81 \times {x}^{8} \times {y}^{12}$

=$81 {x}^{8} {y}^{12}$