Simplify fourth root of x^4y^2z^2

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

Step 1

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

Rewrite $y^{2} z^{2}$ as ${(y z)}^{2}$ .

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

Step 4

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

$x \sqrt{\sqrt{{(y z)}^{2}}}$

Step 5

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

$x \sqrt{y z}$