## Intermediate Algebra (12th Edition)

$\dfrac{8m^{9}n^3}{p^{6}}$
Use the laws of exponents to simplify the given expression, $\left( \dfrac{2m^3n}{p^2}\right)^3 .$ Using the extended Power Rule of the laws of exponents which states that $\left( \dfrac{x^my^n}{z^p} \right)^q=\dfrac{x^{mq}y^{nq}}{z^{pq}},$ the expression above is equivalent to \begin{array}{l}\require{cancel} \dfrac{2^3m^{3(3)}n^3}{p^{2(3)}} \\\\= \dfrac{2^3m^{9}n^3}{p^{6}} \\\\= \dfrac{8m^{9}n^3}{p^{6}} .\end{array}