Simplify fourth root of 32z^8

$\sqrt[4]{32 z^{8}}$

Step 1

Rewrite $32 z^{8}$ as ${(2 z^{2})}^{4} \cdot 2$ .

Factor $16$ out of $32$ .

$\sqrt[4]{16 (2) z^{8}}$

Rewrite $16$ as $2^{4}$ .

$\sqrt[4]{2^{4} \cdot 2 z^{8}}$

Rewrite $z^{8}$ as ${(z^{2})}^{4}$ .

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

Move $2$ .

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

Rewrite $2^{4} {(z^{2})}^{4}$ as ${(2 z^{2})}^{4}$ .

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

Step 2

Pull terms out from under the radical.

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