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