Simplify fifth root of 32z^12

$\sqrt[5]{32 z^{12}}$

Step 1

Rewrite $32 z^{12}$ as ${(2 z^{2})}^{5} z^{2}$ .

Rewrite $32$ as $2^{5}$ .

$\sqrt[5]{2^{5} z^{12}}$

Factor out $z^{10}$ .

$\sqrt[5]{2^{5} (z^{10} z^{2})}$

Rewrite $z^{10}$ as ${(z^{2})}^{5}$ .

$\sqrt[5]{2^{5} ({(z^{2})}^{5} z^{2})}$

Rewrite $2^{5} {(z^{2})}^{5}$ as ${(2 z^{2})}^{5}$ .

$\sqrt[5]{{(2 z^{2})}^{5} z^{2}}$

Step 2

Pull terms out from under the radical.

$2 z^{2} \sqrt[5]{z^{2}}$