Algebra Examples

$(\sqrt[3]{u^{4}}) (\sqrt[3]{2 u^{8}})$

Step 1

Factor out $u^{3}$ .

$\sqrt[3]{u^{3} u} \sqrt[3]{2 u^{8}}$

Step 2

Pull terms out from under the radical.

$u \sqrt[3]{u} \sqrt[3]{2 u^{8}}$

Step 3

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

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Step 3.1

Factor out $u^{6}$ .

$u \sqrt[3]{u} \sqrt[3]{2 (u^{6} u^{2})}$

Step 3.2

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

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

Step 3.3

Reorder $2$ and ${(u^{2})}^{3}$ .

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

Step 3.4

Add parentheses.

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

Step 4

Pull terms out from under the radical.

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

Step 5

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

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Step 5.1

Move $u^{2}$ .

$u^{2} u \sqrt[3]{u} \sqrt[3]{2 u^{2}}$

Step 5.2

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

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Step 5.2.1

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

$u^{2} u^{1} \sqrt[3]{u} \sqrt[3]{2 u^{2}}$

Step 5.2.2

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

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

Step 5.3

Add $2$ and $1$ .

$u^{3} \sqrt[3]{u} \sqrt[3]{2 u^{2}}$

Step 6

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

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Step 6.1

Combine using the product rule for radicals.

$u^{3} \sqrt[3]{2 u^{2} u}$

Step 6.2

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

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

Step 6.3

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

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

Step 6.4

Add $1$ and $2$ .

$u^{3} \sqrt[3]{2 u^{3}}$

Step 7

Reorder $2$ and $u^{3}$ .

$u^{3} \sqrt[3]{u^{3} \cdot 2}$

Step 8

Pull terms out from under the radical.

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

Step 9

Rewrite using the commutative property of multiplication.

$\sqrt[3]{2} u^{3} u$

Step 10

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

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Step 10.1

Move $u$ .

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

Step 10.2

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

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Step 10.2.1

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

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

Step 10.2.2

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

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

Step 10.3

Add $1$ and $3$ .

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