Simplify cube root of (6yz)^6

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

Simplify the expression.

Apply the product rule to $6 y z$ .

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

Apply the product rule to $6 y$ .

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

Raise $6$ to the power of $6$ .

$\sqrt[3]{46656 y^{6} z^{6}}$

Rewrite $46656 y^{6} z^{6}$ as ${(36 y^{2} z^{2})}^{3}$ .

$\sqrt[3]{{(36 y^{2} z^{2})}^{3}}$

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

$36 y^{2} z^{2}$