Simplify the Radical Expression m cube root of 192m^5

$m \sqrt[3]{192 m^{5}}$

Step 1

Rewrite $192 m^{5}$ as ${(4 m)}^{3} \cdot (3 m^{2})$ .

Factor $64$ out of $192$ .

$m \sqrt[3]{64 (3) m^{5}}$

Rewrite $64$ as $4^{3}$ .

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

Factor out $m^{3}$ .

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

Move $3$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

Rewrite using the commutative property of multiplication.

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

Step 4

Multiply $m$ by $m$ by adding the exponents.

Move $m$ .

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

Multiply $m$ by $m$ .

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