Simplify fifth root of 32xy^6z^5

$\sqrt[5]{32 x y^{6} z^{5}}$

Step 1

Rewrite $32 x y^{6} z^{5}$ as ${(2 y z)}^{5} (x y)$ .

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

$\sqrt[5]{2^{5} x y^{6} z^{5}}$

Factor out $y^{5}$ .

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

Move $y$ .

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

Move $x$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

$2 y z \sqrt[5]{x y}$