Answer
$-\dfrac{125x^{21}y^3}{8z^{12}}$
Work Step by Step
Using $\left(\dfrac{a}{b}\right)^x=\dfrac{a^x}{b^x}$, then the expression, $
\left(\dfrac{5x^7y}{-2z^4}\right)^3
$, simplifies to
\begin{array}{l}\require{cancel}
\dfrac{(5x^7y)^3}{(-2z^4)^3}
.\end{array}
Using $(a^x)^y=a^{xy}$, then the given expression, $
\dfrac{(5x^7y)^3}{(-2z^4)^3}
$, simplifies to
\begin{array}{l}\require{cancel}
\dfrac{5^3x^{7(3)}y^3}{(-2)^3z^{4(3)}}
\\\\=
\dfrac{125x^{21}y^3}{-8z^{12}}
\\\\=
-\dfrac{125x^{21}y^3}{8z^{12}}
.\end{array}