Algebra Examples

$(\sqrt[3]{m^{7}}) (\sqrt[3]{5 m^{2}})$

Step 1

Rewrite $m^{7}$ as ${(m^{2})}^{3} m$ .

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Step 1.1

Factor out $m^{6}$ .

$\sqrt[3]{m^{6} m} \sqrt[3]{5 m^{2}}$

Step 1.2

Rewrite $m^{6}$ as ${(m^{2})}^{3}$ .

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

Step 2

Pull terms out from under the radical.

$m^{2} \sqrt[3]{m} \sqrt[3]{5 m^{2}}$

Step 3

Multiply $m^{2} \sqrt[3]{m} \sqrt[3]{5 m^{2}}$ .

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Step 3.1

Combine using the product rule for radicals.

$m^{2} \sqrt[3]{5 m^{2} m}$

Step 3.2

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

$m^{2} \sqrt[3]{5 (m^{1} m^{2})}$

Step 3.3

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

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

Step 3.4

Add $1$ and $2$ .

$m^{2} \sqrt[3]{5 m^{3}}$

Step 4

Reorder $5$ and $m^{3}$ .

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

Step 5

Pull terms out from under the radical.

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

Step 6

Rewrite using the commutative property of multiplication.

$\sqrt[3]{5} m^{2} m$

Step 7

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

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Step 7.1

Move $m$ .

$\sqrt[3]{5} (m \cdot m^{2})$

Step 7.2

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

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Step 7.2.1

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

$\sqrt[3]{5} (m^{1} m^{2})$

Step 7.2.2

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

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

Step 7.3

Add $1$ and $2$ .

$\sqrt[3]{5} m^{3}$