Basic Math Examples

$\sqrt[5]{a^{4} b} \cdot \sqrt[5]{a^{16} b}$

Step 1

Rewrite $a^{16} b$ as ${(a^{3})}^{5} (a b)$ .

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Step 1.1

Factor out $a^{15}$ .

$\sqrt[5]{a^{4} b} \cdot \sqrt[5]{a^{15} a b}$

Step 1.2

Rewrite $a^{15}$ as ${(a^{3})}^{5}$ .

$\sqrt[5]{a^{4} b} \cdot \sqrt[5]{{(a^{3})}^{5} a b}$

Step 1.3

Add parentheses.

$\sqrt[5]{a^{4} b} \cdot \sqrt[5]{{(a^{3})}^{5} (a b)}$

Step 2

Pull terms out from under the radical.

$\sqrt[5]{a^{4} b} \cdot (a^{3} \sqrt[5]{a b})$

Step 3

Multiply $\sqrt[5]{a^{4} b} (a^{3} \sqrt[5]{a b})$ .

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Step 3.1

Combine using the product rule for radicals.

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

Step 3.2

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

$a^{3} \sqrt[5]{a^{1} a^{4} b \cdot b}$

Step 3.3

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

$a^{3} \sqrt[5]{a^{1 + 4} b \cdot b}$

Step 3.4

Add $1$ and $4$ .

$a^{3} \sqrt[5]{a^{5} b \cdot b}$

Step 3.5

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

$a^{3} \sqrt[5]{a^{5} (b^{1} b)}$

Step 3.6

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

$a^{3} \sqrt[5]{a^{5} (b^{1} b^{1})}$

Step 3.7

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

$a^{3} \sqrt[5]{a^{5} b^{1 + 1}}$

Step 3.8

Add $1$ and $1$ .

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

Step 4

Pull terms out from under the radical.

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

Step 5

Multiply $a^{3}$ by $a$ by adding the exponents.

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Step 5.1

Move $a$ .

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

Step 5.2

Multiply $a$ by $a^{3}$ .

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Step 5.2.1

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

$a^{1} a^{3} \sqrt[5]{b^{2}}$

Step 5.2.2

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

$a^{1 + 3} \sqrt[5]{b^{2}}$

Step 5.3

Add $1$ and $3$ .

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