Algebra Examples

$5 \sqrt[3]{9 y^{2}} \cdot \sqrt[3]{24 y}$

Step 1

Rewrite $24 y$ as $2^{3} \cdot (3 y)$ .

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Step 1.1

Factor $8$ out of $24$ .

$5 \sqrt[3]{9 y^{2}} \cdot \sqrt[3]{8 (3) y}$

Step 1.2

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

$5 \sqrt[3]{9 y^{2}} \cdot \sqrt[3]{2^{3} \cdot 3 y}$

Step 1.3

Add parentheses.

$5 \sqrt[3]{9 y^{2}} \cdot \sqrt[3]{2^{3} \cdot (3 y)}$

Step 2

Pull terms out from under the radical.

$5 \sqrt[3]{9 y^{2}} \cdot (2 \sqrt[3]{3 y})$

Step 3

Multiply $5 \sqrt[3]{9 y^{2}} (2 \sqrt[3]{3 y})$ .

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Step 3.1

Multiply $2$ by $5$ .

$10 \sqrt[3]{9 y^{2}} \sqrt[3]{3 y}$

Step 3.2

Combine using the product rule for radicals.

$10 \sqrt[3]{3 y (9 y^{2})}$

Step 3.3

Multiply $9$ by $3$ .

$10 \sqrt[3]{27 y \cdot y^{2}}$

Step 3.4

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

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Step 3.4.1

Move $y^{2}$ .

$10 \sqrt[3]{27 (y^{2} y)}$

Step 3.4.2

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

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Step 3.4.2.1

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

$10 \sqrt[3]{27 (y^{2} y^{1})}$

Step 3.4.2.2

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

$10 \sqrt[3]{27 y^{2 + 1}}$

Step 3.4.3

Add $2$ and $1$ .

$10 \sqrt[3]{27 y^{3}}$

Step 4

Rewrite $27 y^{3}$ as ${(3 y)}^{3}$ .

$10 \sqrt[3]{{(3 y)}^{3}}$

Step 5

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

$10 (3 y)$

Step 6

Multiply $3$ by $10$ .

$30 y$