Simplify ( cube root of m^7)( cube root of 5m^2)

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

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

Factor out $m^{6}$ .

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

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

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

Pull terms out from under the radical.

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

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

Combine using the product rule for radicals.

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

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

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

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

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

Add $1$ and $2$ .

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

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

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

Pull terms out from under the radical.

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

Rewrite using the commutative property of multiplication.

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

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

Move $m$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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