Basic Math Examples

$\sqrt[3]{4 y^{2}} \cdot \sqrt[3]{16 y^{4}}$

Step 1

Rewrite $16 y^{4}$ as ${(2 y)}^{3} \cdot (2 y)$ .

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Step 1.1

Factor $8$ out of $16$ .

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

Step 1.2

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

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

Step 1.3

Factor out $y^{3}$ .

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

Step 1.4

Move $2$ .

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

Step 1.5

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

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

Step 1.6

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

Rewrite using the commutative property of multiplication.

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

Step 4

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

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Step 4.1

Combine using the product rule for radicals.

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

Step 4.2

Multiply $2$ by $4$ .

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

Step 4.3

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

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

Step 4.4

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

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

Step 4.5

Add $1$ and $2$ .

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

Step 5

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

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

Step 6

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

$2 (y (2 y))$

Step 7

Multiply $y$ by $y$ by adding the exponents.

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Step 7.1

Move $y$ .

$2 (y \cdot y \cdot 2)$

Step 7.2

Multiply $y$ by $y$ .

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

Step 8

Move $2$ to the left of $y^{2}$ .

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

Step 9

Multiply $2$ by $2$ .

$4 y^{2}$