Algebra Examples

$5 \sqrt[3]{- 3 w^{2}} \cdot 2 \sqrt[3]{36 w^{3}}$

Step 1

Rewrite $- 3 w^{2}$ as ${({(- 1)}^{3})}^{3} \cdot (3 w^{2})$ .

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Step 1.1

Rewrite $- 3$ as $- 1 (3)$ .

$5 \sqrt[3]{- 1 (3) w^{2}} \cdot (2 \sqrt[3]{36 w^{3}})$

Step 1.2

Rewrite $- 1$ as ${(- 1)}^{3}$ .

$5 \sqrt[3]{{(- 1)}^{3} \cdot 3 w^{2}} \cdot (2 \sqrt[3]{36 w^{3}})$

Step 1.3

Rewrite $- 1$ as ${(- 1)}^{3}$ .

$5 \sqrt[3]{{({(- 1)}^{3})}^{3} \cdot 3 w^{2}} \cdot (2 \sqrt[3]{36 w^{3}})$

Step 1.4

Add parentheses.

$5 \sqrt[3]{{({(- 1)}^{3})}^{3} \cdot (3 w^{2})} \cdot (2 \sqrt[3]{36 w^{3}})$

Step 2

Pull terms out from under the radical.

$5 ({(- 1)}^{3} \sqrt[3]{3 w^{2}}) \cdot (2 \sqrt[3]{36 w^{3}})$

Step 3

Simplify the expression.

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Step 3.1

Raise $- 1$ to the power of $3$ .

$5 (- 1 \sqrt[3]{3 w^{2}}) \cdot (2 \sqrt[3]{36 w^{3}})$

Step 3.2

Rewrite $- 1 \sqrt[3]{3 w^{2}}$ as $- \sqrt[3]{3 w^{2}}$ .

$5 (- \sqrt[3]{3 w^{2}}) \cdot (2 \sqrt[3]{36 w^{3}})$

Step 3.3

Multiply $- 1$ by $5$ .

$- 5 \sqrt[3]{3 w^{2}} \cdot (2 \sqrt[3]{36 w^{3}})$

Step 3.4

Reorder $36$ and $w^{3}$ .

$- 5 \sqrt[3]{3 w^{2}} \cdot (2 \sqrt[3]{w^{3} \cdot 36})$

Step 4

Pull terms out from under the radical.

$- 5 \sqrt[3]{3 w^{2}} \cdot (2 (w \sqrt[3]{36}))$

Step 5

Multiply $- 5 \sqrt[3]{3 w^{2}} (2 w \sqrt[3]{36})$ .

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Step 5.1

Multiply $2$ by $- 5$ .

$- 10 \sqrt[3]{3 w^{2}} (w \sqrt[3]{36})$

Step 5.2

Combine using the product rule for radicals.

$- 10 (w \sqrt[3]{3 w^{2} \cdot 36})$

Step 5.3

Multiply $36$ by $3$ .

$- 10 (w \sqrt[3]{108 w^{2}})$

Step 6

Rewrite $108 w^{2}$ as $3^{3} \cdot (4 w^{2})$ .

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Step 6.1

Factor $27$ out of $108$ .

$- 10 (w \sqrt[3]{27 (4) w^{2}})$

Step 6.2

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

$- 10 (w \sqrt[3]{3^{3} \cdot 4 w^{2}})$

Step 6.3

Add parentheses.

$- 10 (w \sqrt[3]{3^{3} \cdot (4 w^{2})})$

Step 7

Pull terms out from under the radical.

$- 10 (w (3 \sqrt[3]{4 w^{2}}))$

Step 8

Simplify the expression.

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Step 8.1

Rewrite using the commutative property of multiplication.

$- 10 (3 w \sqrt[3]{4 w^{2}})$

Step 8.2

Multiply $3$ by $- 10$ .

$- 30 w \sqrt[3]{4 w^{2}}$