Simplify fourth root of (x^4y^8)/(2^12)

$\sqrt[4]{\frac{x^{4} y^{8}}{2^{12}}}$

Raise $2$ to the power of $12$ .

$\sqrt[4]{\frac{x^{4} y^{8}}{4096}}$

Rewrite $x^{4} y^{8}$ as ${(x y^{2})}^{4}$ .

$\sqrt[4]{\frac{{(x y^{2})}^{4}}{4096}}$

Rewrite $4096$ as $8^{4}$ .

$\sqrt[4]{\frac{{(x y^{2})}^{4}}{8^{4}}}$

Rewrite $\frac{{(x y^{2})}^{4}}{8^{4}}$ as ${(\frac{x y^{2}}{8})}^{4}$ .

$\sqrt[4]{{(\frac{x y^{2}}{8})}^{4}}$

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

$\frac{x y^{2}}{8}$