Basic Math Examples

$\sqrt[3]{5 v^{4}} \cdot \sqrt[3]{25 v^{6}}$

Step 1

Rewrite $5 v^{4}$ as $v^{3} \cdot (5 v)$ .

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Step 1.1

Factor out $v^{3}$ .

$\sqrt[3]{5 (v^{3} v)} \cdot \sqrt[3]{25 v^{6}}$

Step 1.2

Reorder $5$ and $v^{3}$ .

$\sqrt[3]{v^{3} \cdot 5 v} \cdot \sqrt[3]{25 v^{6}}$

Step 1.3

Add parentheses.

$\sqrt[3]{v^{3} \cdot (5 v)} \cdot \sqrt[3]{25 v^{6}}$

Step 2

Pull terms out from under the radical.

$v \sqrt[3]{5 v} \cdot \sqrt[3]{25 v^{6}}$

Step 3

Rewrite $25 v^{6}$ as ${(v^{2})}^{3} \cdot 25$ .

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Step 3.1

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

$v \sqrt[3]{5 v} \cdot \sqrt[3]{25 {(v^{2})}^{3}}$

Step 3.2

Reorder $25$ and ${(v^{2})}^{3}$ .

$v \sqrt[3]{5 v} \cdot \sqrt[3]{{(v^{2})}^{3} \cdot 25}$

Step 4

Pull terms out from under the radical.

$v \sqrt[3]{5 v} \cdot (v^{2} \sqrt[3]{25})$

Step 5

Rewrite using the commutative property of multiplication.

$\sqrt[3]{25} v \sqrt[3]{5 v} v^{2}$

Step 6

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

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Step 6.1

Move $v^{2}$ .

$\sqrt[3]{25} (v^{2} v) \sqrt[3]{5 v}$

Step 6.2

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

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Step 6.2.1

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

$\sqrt[3]{25} (v^{2} v^{1}) \sqrt[3]{5 v}$

Step 6.2.2

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

$\sqrt[3]{25} v^{2 + 1} \sqrt[3]{5 v}$

Step 6.3

Add $2$ and $1$ .

$\sqrt[3]{25} v^{3} \sqrt[3]{5 v}$

Step 7

Multiply $\sqrt[3]{25} v^{3} \sqrt[3]{5 v}$ .

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Step 7.1

Combine using the product rule for radicals.

$v^{3} \sqrt[3]{25 (5 v)}$

Step 7.2

Multiply $25$ by $5$ .

$v^{3} \sqrt[3]{125 v}$

Step 8

Rewrite $125$ as $5^{3}$ .

$v^{3} \sqrt[3]{5^{3} v}$

Step 9

Pull terms out from under the radical.

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

Step 10

Rewrite using the commutative property of multiplication.

$5 v^{3} \sqrt[3]{v}$