Simplify cube root of (8h^4)/27

$\sqrt[3]{\frac{8 h^{4}}{27}}$

Step 1

Rewrite $\frac{8 h^{4}}{27}$ as ${(\frac{2 h}{3})}^{3} h$ .

Factor the perfect power ${(2 h)}^{3}$ out of $8 h^{4}$ .

$\sqrt[3]{\frac{{(2 h)}^{3} h}{27}}$

Factor the perfect power $3^{3}$ out of $27$ .

$\sqrt[3]{\frac{{(2 h)}^{3} h}{3^{3} \cdot 1}}$

Rearrange the fraction $\frac{{(2 h)}^{3} h}{3^{3} \cdot 1}$ .

$\sqrt[3]{{(\frac{2 h}{3})}^{3} h}$

Step 2

Pull terms out from under the radical.

$\frac{2 h}{3} \sqrt[3]{h}$

Step 3

Combine $\frac{2 h}{3}$ and $\sqrt[3]{h}$ .

$\frac{2 h \sqrt[3]{h}}{3}$