Precalculus Examples

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

Step 1

Rewrite $a^{4} b$ as $a^{3} (a b)$ .

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Step 1.1

Factor out $a^{3}$ .

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

Step 1.2

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

Multiply $a \sqrt[3]{a b} \sqrt[3]{a^{2} b}$ .

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Step 3.1

Combine using the product rule for radicals.

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

Step 3.2

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

$a \sqrt[3]{a^{1} a^{2} b \cdot b}$

Step 3.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$a \sqrt[3]{a^{1 + 2} b \cdot b}$

Step 3.4

Add $1$ and $2$ .

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

Step 3.5

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

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

Step 3.6

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

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

Step 3.7

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 3.8

Add $1$ and $1$ .

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

Step 4

Pull terms out from under the radical.

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

Step 5

Multiply $a$ by $a$ by adding the exponents.

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Step 5.1

Move $a$ .

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

Step 5.2

Multiply $a$ by $a$ .

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