Algebra Examples

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

Step 1

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

Tap for more steps...

Step 1.1

Multiply $5$ by $4$ .

$20 \sqrt[3]{4 m^{2}} (m \sqrt[3]{2 m^{2}})$

Step 1.2

Combine using the product rule for radicals.

$20 (m \sqrt[3]{4 m^{2} (2 m^{2})})$

Step 1.3

Multiply $2$ by $4$ .

$20 (m \sqrt[3]{8 m^{2} m^{2}})$

Step 1.4

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

Tap for more steps...

Step 1.4.1

Move $m^{2}$ .

$20 (m \sqrt[3]{8 (m^{2} m^{2})})$

Step 1.4.2

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

$20 (m \sqrt[3]{8 m^{2 + 2}})$

Step 1.4.3

Add $2$ and $2$ .

$20 (m \sqrt[3]{8 m^{4}})$

Step 2

Rewrite $8 m^{4}$ as ${(2 m)}^{3} m$ .

Tap for more steps...

Step 2.1

Rewrite $8$ as $2^{3}$ .

$20 (m \sqrt[3]{2^{3} m^{4}})$

Step 2.2

Factor out $m^{3}$ .

$20 (m \sqrt[3]{2^{3} (m^{3} m)})$

Step 2.3

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

$20 (m \sqrt[3]{{(2 m)}^{3} m})$

Step 3

Pull terms out from under the radical.

$20 (m (2 m \sqrt[3]{m}))$

Step 4

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

Tap for more steps...

Step 4.1

Move $m$ .

$20 (m \cdot m (2 \sqrt[3]{m}))$

Step 4.2

Multiply $m$ by $m$ .

$20 (m^{2} (2 \sqrt[3]{m}))$

Step 5

Rewrite using the commutative property of multiplication.

$20 (2 m^{2} \sqrt[3]{m})$

Step 6

Multiply $2$ by $20$ .

$40 m^{2} \sqrt[3]{m}$