Answer
$\dfrac{8}{x^{12}y^{18}}
$
Work Step by Step
Using laws of exponents, the given expression simpifies to
\begin{align*}
&
\left( \dfrac{5x^7y^4}{10x^3y^{-2}} \right)^{-3}
\\\\&=
\left( \dfrac{x^{7-3}y^{4-(-2)}}{2} \right)^{-3}
\\\\&=
\left( \dfrac{x^{4}y^{6}}{2} \right)^{-3}
\\\\&=
\dfrac{x^{4(-3)}y^{6(-3)}}{2^{-3}}
\\\\&=
\dfrac{x^{-12}y^{-18}}{2^{-3}}
\\\\&=
\dfrac{2^{3}}{x^{12}y^{18}}
\\\\&=
\dfrac{8}{x^{12}y^{18}}
.\end{align*}
