Simplify fourth root of (32w)/81

$\sqrt[4]{\frac{32 w}{81}}$

Rewrite $\frac{32 w}{81}$ as ${(\frac{2}{3})}^{4} (2 w)$ .

Factor the perfect power $2^{4}$ out of $32 w$ .

$\sqrt[4]{\frac{2^{4} \cdot (2 w)}{81}}$

Factor the perfect power $3^{4}$ out of $81$ .

$\sqrt[4]{\frac{2^{4} \cdot (2 w)}{3^{4} \cdot 1}}$

Rearrange the fraction $\frac{2^{4} \cdot (2 w)}{3^{4} \cdot 1}$ .

$\sqrt[4]{{(\frac{2}{3})}^{4} (2 w)}$

Pull terms out from under the radical.

$\frac{2}{3} \sqrt[4]{2 w}$

Combine $\frac{2}{3}$ and $\sqrt[4]{2 w}$ .

$\frac{2 \sqrt[4]{2 w}}{3}$