Simplify the Radical Expression fourth root of 256x^2y^16

$\sqrt[4]{256 x^{2} y^{16}}$

Rewrite $256 x^{2} y^{16}$ as ${(4 y^{4})}^{4} x^{2}$ .

Rewrite $256$ as $4^{4}$ .

$\sqrt[4]{4^{4} x^{2} y^{16}}$

Rewrite $y^{16}$ as ${(y^{4})}^{4}$ .

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

Move $x^{2}$ .

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

Rewrite $4^{4} {(y^{4})}^{4}$ as ${(4 y^{4})}^{4}$ .

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

Pull terms out from under the radical.

$| 4 y^{4} | \sqrt[4]{x^{2}}$

Remove non-negative terms from the absolute value.

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

Rewrite $\sqrt[4]{x^{2}}$ as $\sqrt{\sqrt{x^{2}}}$ .

$4 y^{4} \sqrt{\sqrt{x^{2}}}$

Pull terms out from under the radical.

$4 y^{4} \sqrt{| x |}$