Finite Math Examples

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

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $4 a b^{5}$ as $b^{3} \cdot (4 a b^{2})$ .

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Step 1.1.1

Factor out $b^{3}$ .

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

Step 1.1.2

Move $a$ .

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

Step 1.1.3

Reorder $4$ and $b^{3}$ .

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

Step 1.1.4

Add parentheses.

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

Step 1.1.5

Add parentheses.

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

Step 1.2

Pull terms out from under the radical.

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

Step 2

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

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Step 2.1

Factor $b$ out of $b \sqrt[3]{4 a b^{2}}$ .

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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