Simplify cube root of (8m^3n^6)/27

$\sqrt[3]{\frac{8 m^{3} n^{6}}{27}}$

Rewrite $8 m^{3} n^{6}$ as ${(2 m n^{2})}^{3}$ .

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

Rewrite $27$ as $3^{3}$ .

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

Rewrite $\frac{{(2 m n^{2})}^{3}}{3^{3}}$ as ${(\frac{2 m n^{2}}{3})}^{3}$ .

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

Pull terms out from under the radical, assuming real numbers.

$\frac{2 m n^{2}}{3}$