Basic Math Examples

$\sqrt[3]{2 n y^{2}} \cdot \sqrt[3]{4 n^{2} y^{7}}$

Step 1

Rewrite $4 n^{2} y^{7}$ as ${(y^{2})}^{3} \cdot (4 n^{2} y)$ .

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Step 1.1

Factor out $y^{6}$ .

$\sqrt[3]{2 n y^{2}} \cdot \sqrt[3]{4 n^{2} (y^{6} y)}$

Step 1.2

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

$\sqrt[3]{2 n y^{2}} \cdot \sqrt[3]{4 n^{2} ({(y^{2})}^{3} y)}$

Step 1.3

Move $n^{2}$ .

$\sqrt[3]{2 n y^{2}} \cdot \sqrt[3]{4 {(y^{2})}^{3} n^{2} y}$

Step 1.4

Reorder $4$ and ${(y^{2})}^{3}$ .

$\sqrt[3]{2 n y^{2}} \cdot \sqrt[3]{{(y^{2})}^{3} \cdot 4 n^{2} y}$

Step 1.5

Add parentheses.

$\sqrt[3]{2 n y^{2}} \cdot \sqrt[3]{{(y^{2})}^{3} \cdot 4 (n^{2} y)}$

Step 1.6

Add parentheses.

$\sqrt[3]{2 n y^{2}} \cdot \sqrt[3]{{(y^{2})}^{3} \cdot (4 n^{2} y)}$

Step 2

Pull terms out from under the radical.

$\sqrt[3]{2 n y^{2}} \cdot (y^{2} \sqrt[3]{4 n^{2} y})$

Step 3

Multiply $\sqrt[3]{2 n y^{2}} (y^{2} \sqrt[3]{4 n^{2} y})$ .

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Step 3.1

Combine using the product rule for radicals.

$y^{2} \sqrt[3]{2 n y^{2} (4 n^{2} y)}$

Step 3.2

Multiply $4$ by $2$ .

$y^{2} \sqrt[3]{8 n y^{2} (n^{2} y)}$

Step 3.3

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

$y^{2} \sqrt[3]{8 (n^{2} n^{1}) y^{2} y}$

Step 3.4

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

$y^{2} \sqrt[3]{8 n^{2 + 1} y^{2} y}$

Step 3.5

Add $2$ and $1$ .

$y^{2} \sqrt[3]{8 n^{3} y^{2} y}$

Step 3.6

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

$y^{2} \sqrt[3]{8 n^{3} (y^{1} y^{2})}$

Step 3.7

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

$y^{2} \sqrt[3]{8 n^{3} y^{1 + 2}}$

Step 3.8

Add $1$ and $2$ .

$y^{2} \sqrt[3]{8 n^{3} y^{3}}$

Step 4

Rewrite $8 n^{3} y^{3}$ as ${(2 n y)}^{3}$ .

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

Step 5

Pull terms out from under the radical, assuming real numbers.

$y^{2} (2 n y)$

Step 6

Rewrite using the commutative property of multiplication.

$2 y^{2} (n y)$

Step 7

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

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Step 7.1

Move $y$ .

$2 (y \cdot y^{2}) n$

Step 7.2

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

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Step 7.2.1

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

$2 (y^{1} y^{2}) n$

Step 7.2.2

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

$2 y^{1 + 2} n$

Step 7.3

Add $1$ and $2$ .

$2 y^{3} n$