Algebra Examples

$- 2 \sqrt[3]{6 y} (- 5 \sqrt[3]{9 y^{2}})$

Step 1

Multiply $- 2 \sqrt[3]{6 y} (- 5 \sqrt[3]{9 y^{2}})$ .

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Step 1.1

Multiply $- 5$ by $- 2$ .

$10 \sqrt[3]{6 y} \sqrt[3]{9 y^{2}}$

Step 1.2

Combine using the product rule for radicals.

$10 \sqrt[3]{9 y^{2} (6 y)}$

Step 1.3

Multiply $6$ by $9$ .

$10 \sqrt[3]{54 y^{2} y}$

Step 1.4

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

$10 \sqrt[3]{54 (y^{1} y^{2})}$

Step 1.5

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

$10 \sqrt[3]{54 y^{1 + 2}}$

Step 1.6

Add $1$ and $2$ .

$10 \sqrt[3]{54 y^{3}}$

Step 2

Rewrite $54 y^{3}$ as ${(3 y)}^{3} \cdot 2$ .

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Step 2.1

Factor $27$ out of $54$ .

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

Step 2.2

Rewrite $27$ as $3^{3}$ .

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

Step 2.3

Move $2$ .

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

Step 2.4

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

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

Step 3

Pull terms out from under the radical.

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

Step 4

Multiply $3$ by $10$ .

$30 y \sqrt[3]{2}$