Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

Cancel the common factor.

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

Step 1.4

Rewrite the expression.

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

Step 2

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

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Step 2.1

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

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

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

Step 3.2.2

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

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

Step 3.2.3

Cancel the common factor.

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

Step 3.2.4

Rewrite the expression.

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

Step 3.2.5

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

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

Step 4

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

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

Step 5

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

$2 a b$