Answer
$\dfrac{m^{6}}{8n^{9}}$
Work Step by Step
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}
