Simplify cube root of (32a^5b^4)/(4a^2b)

$\sqrt[3]{\frac{32 a^{5} b^{4}}{4 a^{2} b}}$

Reduce the expression $\frac{32 a^{5} b^{4}}{4 a^{2} b}$ by cancelling the common factors.

Factor $4$ out of $32 a^{5} b^{4}$ .

$\sqrt[3]{\frac{4 (8 a^{5} b^{4})}{4 a^{2} b}}$

Factor $4$ out of $4 a^{2} b$ .

$\sqrt[3]{\frac{4 (8 a^{5} b^{4})}{4 (a^{2} b)}}$

Cancel the common factor.

$\sqrt[3]{\frac{4 (8 a^{5} b^{4})}{4 (a^{2} b)}}$

Rewrite the expression.

$\sqrt[3]{\frac{8 a^{5} b^{4}}{a^{2} b}}$

Cancel the common factor of $a^{5}$ and $a^{2}$ .

Factor $a^{2}$ out of $8 a^{5} b^{4}$ .

$\sqrt[3]{\frac{a^{2} (8 a^{3} b^{4})}{a^{2} b}}$

Cancel the common factors.

Factor $a^{2}$ out of $a^{2} b$ .

$\sqrt[3]{\frac{a^{2} (8 a^{3} b^{4})}{a^{2} (b)}}$

Cancel the common factor.

$\sqrt[3]{\frac{a^{2} (8 a^{3} b^{4})}{a^{2} b}}$

Rewrite the expression.

$\sqrt[3]{\frac{8 a^{3} b^{4}}{b}}$

Cancel the common factor of $b^{4}$ and $b$ .

Factor $b$ out of $8 a^{3} b^{4}$ .

$\sqrt[3]{\frac{b (8 a^{3} b^{3})}{b}}$

Cancel the common factors.

Raise $b$ to the power of $1$ .

$\sqrt[3]{\frac{b (8 a^{3} b^{3})}{b^{1}}}$

Factor $b$ out of $b^{1}$ .

$\sqrt[3]{\frac{b (8 a^{3} b^{3})}{b \cdot 1}}$

Cancel the common factor.

$\sqrt[3]{\frac{b (8 a^{3} b^{3})}{b \cdot 1}}$

Rewrite the expression.

$\sqrt[3]{\frac{8 a^{3} b^{3}}{1}}$

Divide $8 a^{3} b^{3}$ by $1$ .

$\sqrt[3]{8 a^{3} b^{3}}$

Rewrite $8 a^{3} b^{3}$ as ${(2 a b)}^{3}$ .

$\sqrt[3]{{(2 a b)}^{3}}$

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

$2 a b$