Simplify cube root of 27x^4y^5z^3

$\sqrt[3]{27 x^{4} \cdot y^{5} \cdot z^{3}}$

Rewrite $27 x^{4} \cdot y^{5} \cdot z^{3}$ as ${(3 x y z)}^{3} (x y^{2})$ .

Rewrite $27$ as $3^{3}$ .

$\sqrt[3]{3^{3} x^{4} \cdot y^{5} \cdot z^{3}}$

Factor out $x^{3}$ .

$\sqrt[3]{3^{3} (x^{3} x) \cdot y^{5} \cdot z^{3}}$

Factor out $y^{3}$ .

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

Move $y^{2}$ .

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

Move $x$ .

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

Rewrite $(3^{3} (x^{3}) \cdot (y^{3})) \cdot z^{3}$ as ${(3 x y z)}^{3}$ .

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

Add parentheses.

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

Pull terms out from under the radical.

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

Simplify cube root of 27x^4*y^5*z^3