Simplify cube root of 54m^8* cube root of 5m^4

$\sqrt[3]{54 m^{8}} \cdot \sqrt[3]{5 m^{4}}$

Rewrite $54 m^{8}$ as ${(3 m^{2})}^{3} \cdot (2 m^{2})$ .

Factor $27$ out of $54$ .

$\sqrt[3]{27 (2) m^{8}} \cdot \sqrt[3]{5 m^{4}}$

Rewrite $27$ as $3^{3}$ .

$\sqrt[3]{3^{3} \cdot 2 m^{8}} \cdot \sqrt[3]{5 m^{4}}$

Factor out $m^{6}$ .

$\sqrt[3]{3^{3} \cdot 2 (m^{6} m^{2})} \cdot \sqrt[3]{5 m^{4}}$

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

$\sqrt[3]{3^{3} \cdot 2 ({(m^{2})}^{3} m^{2})} \cdot \sqrt[3]{5 m^{4}}$

Move $2$ .

$\sqrt[3]{3^{3} {(m^{2})}^{3} \cdot 2 m^{2}} \cdot \sqrt[3]{5 m^{4}}$

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

$\sqrt[3]{{(3 m^{2})}^{3} \cdot 2 m^{2}} \cdot \sqrt[3]{5 m^{4}}$

Add parentheses.

$\sqrt[3]{{(3 m^{2})}^{3} \cdot (2 m^{2})} \cdot \sqrt[3]{5 m^{4}}$

Pull terms out from under the radical.

$3 m^{2} \sqrt[3]{2 m^{2}} \cdot \sqrt[3]{5 m^{4}}$

Rewrite $5 m^{4}$ as $m^{3} \cdot (5 m)$ .

Factor out $m^{3}$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

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

Move $m$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

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

Combine using the product rule for radicals.

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

Multiply $2$ by $5$ .

$3 m^{3} \sqrt[3]{10 m \cdot m^{2}}$

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

Move $m^{2}$ .

$3 m^{3} \sqrt[3]{10 (m^{2} m)}$

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

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

$3 m^{3} \sqrt[3]{10 (m^{2} m^{1})}$

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

$3 m^{3} \sqrt[3]{10 m^{2 + 1}}$

Add $2$ and $1$ .

$3 m^{3} \sqrt[3]{10 m^{3}}$

Reorder $10$ and $m^{3}$ .

$3 m^{3} \sqrt[3]{m^{3} \cdot 10}$

Pull terms out from under the radical.

$3 m^{3} (m \sqrt[3]{10})$

Multiply $m^{3}$ by $m$ by adding the exponents.

Move $m$ .

$3 (m \cdot m^{3}) \sqrt[3]{10}$

Multiply $m$ by $m^{3}$ .

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

$3 (m^{1} m^{3}) \sqrt[3]{10}$

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

$3 m^{1 + 3} \sqrt[3]{10}$

Add $1$ and $3$ .

$3 m^{4} \sqrt[3]{10}$

Simplify cube root of 54m^8* cube root of 5m^4

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