Answer
$\dfrac{2x}{z\sqrt[3]{2x^2z}}$
Work Step by Step
Rationalizing the numerator of $
\dfrac{\sqrt[3]{4x}}{\sqrt[3]{z^4}}
$ results to
\begin{array}{l}
\dfrac{\sqrt[3]{4x}}{z\sqrt[3]{z}}
\cdot
\dfrac{\sqrt[3]{2x^2}}{\sqrt[3]{2x^2}}
\\\\=
\dfrac{\sqrt[3]{8x^3}}{z\sqrt[3]{2x^2z}}
\\\\=
\dfrac{2x}{z\sqrt[3]{2x^2z}}
.\end{array}