Finite Math Examples

$\sqrt{m} \sqrt[4]{m^{17}}$

Step 1

Rewrite $m^{17}$ as ${(m^{4})}^{4} m$ .

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Step 1.1

Factor out $m^{16}$ .

$\sqrt{m} \sqrt[4]{m^{16} m}$

Step 1.2

Rewrite $m^{16}$ as ${(m^{4})}^{4}$ .

$\sqrt{m} \sqrt[4]{{(m^{4})}^{4} m}$

Step 2

Pull terms out from under the radical.

$\sqrt{m} (m^{4} \sqrt[4]{m})$

Step 3

Multiply $\sqrt{m} (m^{4} \sqrt[4]{m})$ .

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Step 3.1

Rewrite the expression using the least common index of $4$ .

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Step 3.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{m}$ as $m^{\frac{1}{2}}$ .

$m^{4} (m^{\frac{1}{2}} \sqrt[4]{m})$

Step 3.1.2

Rewrite $m^{\frac{1}{2}}$ as $m^{\frac{2}{4}}$ .

$m^{4} (m^{\frac{2}{4}} \sqrt[4]{m})$

Step 3.1.3

Rewrite $m^{\frac{2}{4}}$ as $\sqrt[4]{m^{2}}$ .

$m^{4} (\sqrt[4]{m^{2}} \sqrt[4]{m})$

Step 3.2

Combine using the product rule for radicals.

$m^{4} \sqrt[4]{m^{2} m}$

Step 3.3

Multiply $m^{2}$ by $m$ by adding the exponents.

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Step 3.3.1

Multiply $m^{2}$ by $m$ .

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Step 3.3.1.1

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

$m^{4} \sqrt[4]{m^{2} m^{1}}$

Step 3.3.1.2

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

$m^{4} \sqrt[4]{m^{2 + 1}}$

Step 3.3.2

Add $2$ and $1$ .

$m^{4} \sqrt[4]{m^{3}}$