Simplify cube root of xy^5z^20

$\sqrt[3]{x y^{5} z^{20}}$

Rewrite $x y^{5} z^{20}$ as ${(y z^{6})}^{3} (x y^{2} z^{2})$ .

Factor out $y^{3}$ .

$\sqrt[3]{x (y^{3} y^{2}) z^{20}}$

Factor out $z^{18}$ .

$\sqrt[3]{x (y^{3} y^{2}) (z^{18} z^{2})}$

Rewrite $z^{18}$ as ${(z^{6})}^{3}$ .

$\sqrt[3]{x (y^{3} y^{2}) ({(z^{6})}^{3} z^{2})}$

Move $y^{2}$ .

$\sqrt[3]{x (y^{3}) {(z^{6})}^{3} y^{2} z^{2}}$

Move $x$ .

$\sqrt[3]{y^{3} {(z^{6})}^{3} x y^{2} z^{2}}$

Rewrite $(y^{3}) {(z^{6})}^{3}$ as ${(y z^{6})}^{3}$ .

$\sqrt[3]{{(y z^{6})}^{3} x y^{2} z^{2}}$

Add parentheses.

$\sqrt[3]{{(y z^{6})}^{3} x (y^{2} z^{2})}$

Add parentheses.

$\sqrt[3]{{(y z^{6})}^{3} (x y^{2} z^{2})}$

Pull terms out from under the radical.

$y z^{6} \sqrt[3]{x y^{2} z^{2}}$