Simplify the Radical Expression eighth root of x^2y^6

$\sqrt[8]{x^{2} y^{6}}$

Rewrite $x^{2} y^{6}$ as ${(x y^{3})}^{2}$ .

$\sqrt[8]{{(x y^{3})}^{2}}$

Rewrite $\sqrt[8]{{(x y^{3})}^{2}}$ as $\sqrt[4]{\sqrt{{(x y^{3})}^{2}}}$ .

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

Pull terms out from under the radical.

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