Answer
$\dfrac{x^{8}y^4}{z^{12}}$
Work Step by Step
Using $\left(\dfrac{a}{b}\right)^x=\dfrac{a^x}{b^x}$, then the expression, $
\left(\dfrac{x^2y}{z^3}\right)^4
$, simplifies to
\begin{array}{l}\require{cancel}
\dfrac{(x^2y)^4}{(z^3)^4}
.\end{array}
Using $(a^x)^y=a^{xy}$, then the given expression, $
\dfrac{(x^2y)^4}{(z^3)^4}
$, simplifies to
\begin{array}{l}\require{cancel}
\dfrac{x^{2(4)}y^4}{z^{3(4)}}
\\\\=
\dfrac{x^{8}y^4}{z^{12}}
.\end{array}