Simplify eighth root of x^4y^4

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

Step 1

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

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

Step 2

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

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

Step 3

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

$\sqrt{x y}$