Answer
$\frac{2\sqrt[3] {25g^2}}{75g}$.
Work Step by Step
The given expression is
$=\frac{2\sqrt[3] {gh}}{15\sqrt[3]{5g^2h}}$
Use division rule.
$=\frac{2}{15}\sqrt[3] {\frac{gh}{5g^2h}}$
Reduce the fraction.
$=\frac{2}{15}\sqrt[3] {\frac{1}{5g}}$
Multiply by the needed factors.
$=\frac{2}{15}\sqrt[3] {\frac{1}{5g}}\cdot \sqrt[3] {\frac{5^2g^2}{5^2g^2}}$
Use multiplication rule.
$=\frac{2}{15}\sqrt[3] {\frac{5^2g^2}{5g\cdot 5^2g^2}}$
Simplify.
$=\frac{2}{15}\sqrt[3] {\frac{5^2g^2}{ 5^3g^3}}$
Cube root the denominator.
$=\frac{2\sqrt[3] {5^2g^2}}{15\cdot 5g}$
Simplify.
$=\frac{2\sqrt[3] {25g^2}}{75g}$.
