Simplify cube root of 10w^5* cube root of 4w^4

$\sqrt[3]{10 w^{5}} \times \sqrt[3]{4 w^{4}}$

Step 1

Rewrite $10 w^{5}$ as $w^{3} \cdot (10 w^{2})$ .

Factor out $w^{3}$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

Factor out $w^{3}$ .

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

Reorder $4$ and $w^{3}$ .

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

Add parentheses.

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

Step 4

Pull terms out from under the radical.

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

Step 5

Multiply $w$ by $w$ by adding the exponents.

Move $w$ .

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

Multiply $w$ by $w$ .

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

Step 6

Multiply $w^{2} \sqrt[3]{10 w^{2}} \sqrt[3]{4 w}$ .

Combine using the product rule for radicals.

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

Multiply $10$ by $4$ .

$w^{2} \sqrt[3]{40 w \cdot w^{2}}$

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

Move $w^{2}$ .

$w^{2} \sqrt[3]{40 (w^{2} w)}$

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

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

$w^{2} \sqrt[3]{40 (w^{2} w^{1})}$

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

$w^{2} \sqrt[3]{40 w^{2 + 1}}$

Add $2$ and $1$ .

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

Step 7

Rewrite $40 w^{3}$ as ${(2 w)}^{3} \cdot 5$ .

Factor $8$ out of $40$ .

$w^{2} \sqrt[3]{8 (5) w^{3}}$

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

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

Move $5$ .

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

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

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

Step 8

Pull terms out from under the radical.

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

Step 9

Rewrite using the commutative property of multiplication.

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

Step 10

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

Move $w$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Simplify cube root of 10w^5* cube root of 4w^4

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