Simplify eighth root of x^2y^4

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

Step 1

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

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

Step 2

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

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

Step 3

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

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