Simplify cube root of (x^3y^12)/64

$\sqrt[3]{\frac{x^{3} y^{12}}{64}}$

Rewrite $x^{3} y^{12}$ as ${(x y^{4})}^{3}$ .

$\sqrt[3]{\frac{{(x y^{4})}^{3}}{64}}$

Rewrite $64$ as $4^{3}$ .

$\sqrt[3]{\frac{{(x y^{4})}^{3}}{4^{3}}}$

Rewrite $\frac{{(x y^{4})}^{3}}{4^{3}}$ as ${(\frac{x y^{4}}{4})}^{3}$ .

$\sqrt[3]{{(\frac{x y^{4}}{4})}^{3}}$

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

$\frac{x y^{4}}{4}$