# How do you multiply (-5x^4y^2)^3?

Apr 10, 2015

First of all, refer to the Index law of ${\left({a}^{m}\right)}^{n} = {a}^{m n}$

This means when there's a power of a power, the powers are multiplied. e.g. ${\left({2}^{4}\right)}^{2} = {2}^{4 \times 2} = {2}^{8}$

${\left(- 5 {x}^{4} {y}^{2}\right)}^{3}$:

We have to multiply all the powers of the values within the bracket by 3 thus.

${\left(- 5 {x}^{4} {y}^{2}\right)}^{3}$= ${\left(- 5\right)}^{3} {x}^{4 \times 3} {y}^{2 \times 3} = - 125 {x}^{12} {y}^{6}$

$- 125 {x}^{12} {y}^{6}$ is thus the answer.