Basic Math Examples

$\sqrt[4]{m^{5}} \cdot \sqrt[5]{m^{2}}$

Step 1

Factor out $m^{4}$ .

$\sqrt[4]{m^{4} m} \cdot \sqrt[5]{m^{2}}$

Step 2

Pull terms out from under the radical.

$m \sqrt[4]{m} \cdot \sqrt[5]{m^{2}}$

Step 3

Multiply $m \sqrt[4]{m} \sqrt[5]{m^{2}}$ .

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Step 3.1

Rewrite the expression using the least common index of $20$ .

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Step 3.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{m^{2}}$ as $m^{\frac{2}{5}}$ .

$m (m^{\frac{2}{5}} \sqrt[4]{m})$

Step 3.1.2

Rewrite $m^{\frac{2}{5}}$ as $m^{\frac{8}{20}}$ .

$m (m^{\frac{8}{20}} \sqrt[4]{m})$

Step 3.1.3

Rewrite $m^{\frac{8}{20}}$ as $\sqrt[20]{m^{8}}$ .

$m (\sqrt[20]{m^{8}} \sqrt[4]{m})$

Step 3.1.4

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{m}$ as $m^{\frac{1}{4}}$ .

$m (\sqrt[20]{m^{8}} m^{\frac{1}{4}})$

Step 3.1.5

Rewrite $m^{\frac{1}{4}}$ as $m^{\frac{5}{20}}$ .

$m (\sqrt[20]{m^{8}} m^{\frac{5}{20}})$

Step 3.1.6

Rewrite $m^{\frac{5}{20}}$ as $\sqrt[20]{m^{5}}$ .

$m (\sqrt[20]{m^{8}} \sqrt[20]{m^{5}})$

Step 3.2

Combine using the product rule for radicals.

$m \sqrt[20]{m^{8} m^{5}}$

Step 3.3

Multiply $m^{8}$ by $m^{5}$ by adding the exponents.

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Step 3.3.1

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

$m \sqrt[20]{m^{8 + 5}}$

Step 3.3.2

Add $8$ and $5$ .

$m \sqrt[20]{m^{13}}$