Simplify ( cube root of 64m^3)( cube root of 15m^6)

$(\sqrt[3]{64 m^{3}}) (\sqrt[3]{15 m^{6}})$

Rewrite $64 m^{3}$ as ${(4 m)}^{3}$ .

$\sqrt[3]{{(4 m)}^{3}} \sqrt[3]{15 m^{6}}$

Pull terms out from under the radical, assuming real numbers.

$4 m \sqrt[3]{15 m^{6}}$

Rewrite $15 m^{6}$ as ${(m^{2})}^{3} \cdot 15$ .

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

$4 m \sqrt[3]{15 {(m^{2})}^{3}}$

Reorder $15$ and ${(m^{2})}^{3}$ .

$4 m \sqrt[3]{{(m^{2})}^{3} \cdot 15}$

Pull terms out from under the radical.

$4 m (m^{2} \sqrt[3]{15})$

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

Move $m^{2}$ .

$4 (m^{2} m) \sqrt[3]{15}$

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

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

$4 (m^{2} m^{1}) \sqrt[3]{15}$

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

$4 m^{2 + 1} \sqrt[3]{15}$

Add $2$ and $1$ .

$4 m^{3} \sqrt[3]{15}$