#### Answer

$\sqrt[5]{\dfrac{512y^3z^3}{343x^3}}$

#### Work Step by Step

Using the laws of exponents, the given expression, $
\left( \dfrac{7x}{8yz} \right)^{-3/5}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\left( \dfrac{8yz}{7x} \right)^{3/5}
.\end{array}
Using $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the expression, $
\left( \dfrac{8yz}{7x} \right)^{3/5}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt[5]{\left( \dfrac{8yz}{7x} \right)^{3}}
\\\\=
\sqrt[5]{\dfrac{8^3y^3z^3}{7^3x^3}}
\\\\=
\sqrt[5]{\dfrac{512y^3z^3}{343x^3}}
.\end{array}