Basic Math Examples

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

Step 1

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

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Step 1.1

Combine using the product rule for radicals.

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

Step 1.2

Multiply $4$ by $2$ .

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

Step 2

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

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

Step 3

Pull terms out from under the radical.

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

Step 4

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

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Step 4.1

Combine using the product rule for radicals.

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

Step 4.2

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

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

Step 4.3

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

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

Step 4.4

Add $1$ and $2$ .

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

Step 5

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

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

Step 6

Pull terms out from under the radical.

$2 y \sqrt[3]{2}$