## Intermediate Algebra (12th Edition)

$\dfrac{m^{6}}{8n^{9}}$
Use the laws of exponents to simplify the given expression, $(2m^{-2}n^3)^{-3} .$ Using the extended Power Rule of the laws of exponents which states that $\left( x^my^n \right)^p=x^{mp}y^{np},$ the expression above is equivalent to \begin{array}{l}\require{cancel} 2^{-3}m^{-2(-3)}n^{3(-3)} \\\\= 2^{-3}m^{6}n^{-9} .\end{array} Using the Negative Exponent Rule of the laws of exponents which states that $x^{-m}=\dfrac{1}{x^m}$ or $\dfrac{1}{x^{-m}}=x^m,$ the expression above is equivalent to \begin{array}{l}\require{cancel} \dfrac{m^{6}}{2^{3}n^{9}} \\\\= \dfrac{m^{6}}{8n^{9}} .\end{array}