Basic Math Examples

$\sqrt[3]{5 n^{2}} \cdot \sqrt[3]{7 n^{5}}$

Step 1

Rewrite $7 n^{5}$ as $n^{3} \cdot (7 n^{2})$ .

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Step 1.1

Factor out $n^{3}$ .

$\sqrt[3]{5 n^{2}} \cdot \sqrt[3]{7 (n^{3} n^{2})}$

Step 1.2

Reorder $7$ and $n^{3}$ .

$\sqrt[3]{5 n^{2}} \cdot \sqrt[3]{n^{3} \cdot 7 n^{2}}$

Step 1.3

Add parentheses.

$\sqrt[3]{5 n^{2}} \cdot \sqrt[3]{n^{3} \cdot (7 n^{2})}$

Step 2

Pull terms out from under the radical.

$\sqrt[3]{5 n^{2}} \cdot (n \sqrt[3]{7 n^{2}})$

Step 3

Multiply $\sqrt[3]{5 n^{2}} (n \sqrt[3]{7 n^{2}})$ .

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Step 3.1

Combine using the product rule for radicals.

$n \sqrt[3]{5 n^{2} (7 n^{2})}$

Step 3.2

Multiply $7$ by $5$ .

$n \sqrt[3]{35 n^{2} n^{2}}$

Step 3.3

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

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Step 3.3.1

Move $n^{2}$ .

$n \sqrt[3]{35 (n^{2} n^{2})}$

Step 3.3.2

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

$n \sqrt[3]{35 n^{2 + 2}}$

Step 3.3.3

Add $2$ and $2$ .

$n \sqrt[3]{35 n^{4}}$

Step 4

Rewrite $35 n^{4}$ as $n^{3} \cdot (35 n)$ .

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Step 4.1

Factor out $n^{3}$ .

$n \sqrt[3]{35 (n^{3} n)}$

Step 4.2

Reorder $35$ and $n^{3}$ .

$n \sqrt[3]{n^{3} \cdot 35 n}$

Step 4.3

Add parentheses.

$n \sqrt[3]{n^{3} \cdot (35 n)}$

Step 5

Pull terms out from under the radical.

$n (n \sqrt[3]{35 n})$

Step 6

Multiply $n$ by $n$ by adding the exponents.

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Step 6.1

Move $n$ .

$n \cdot n \sqrt[3]{35 n}$

Step 6.2

Multiply $n$ by $n$ .

$n^{2} \sqrt[3]{35 n}$