Simplify the Radical Expression sixth root of 16x^2y^4

$\sqrt[6]{16 x^{2} y^{4}}$

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

$\sqrt[6]{{(4 x y^{2})}^{2}}$

Rewrite $\sqrt[6]{{(4 x y^{2})}^{2}}$ as $\sqrt[3]{\sqrt{{(4 x y^{2})}^{2}}}$ .

$\sqrt[3]{\sqrt{{(4 x y^{2})}^{2}}}$

Pull terms out from under the radical.

$\sqrt[3]{| 4 x y^{2} |}$

Remove non-negative terms from the absolute value.

$\sqrt[3]{4 y^{2} | x |}$