Answer
$\frac{2h\sqrt[3]{h}}{3}$.
Work Step by Step
The given expression is
$=\sqrt[3]{\frac{8h^4}{27}}$
Use quotient property of cube roots.
$=\frac{\sqrt[3]{8h^4}}{\sqrt[3]{27}}$
Factor as cube terms.
$=\frac{\sqrt[3]{8h^3\cdot h}}{\sqrt[3]{27}}$
Use prodcut property of cube roots.
$=\frac{\sqrt[3]{8}\cdot\sqrt[3]{h^3}\cdot \sqrt[3]{h}}{\sqrt[3]{27}}$
Use $8=2^3$ and $27=3^3$.
$=\frac{\sqrt[3]{2^3}\cdot\sqrt[3]{h^3}\cdot \sqrt[3]{h}}{\sqrt[3]{3^3}}$
Simplify.
$=\frac{2h\sqrt[3]{h}}{3}$.