Algebra Examples

$5 \sqrt[3]{9 a^{2}} \cdot 4 \sqrt[3]{3 a}$

Step 1

Multiply $5 \sqrt[3]{9 a^{2}} (4 \sqrt[3]{3 a})$ .

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Step 1.1

Multiply $4$ by $5$ .

$20 \sqrt[3]{9 a^{2}} \sqrt[3]{3 a}$

Step 1.2

Combine using the product rule for radicals.

$20 \sqrt[3]{3 a (9 a^{2})}$

Step 1.3

Multiply $9$ by $3$ .

$20 \sqrt[3]{27 a \cdot a^{2}}$

Step 1.4

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

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Step 1.4.1

Move $a^{2}$ .

$20 \sqrt[3]{27 (a^{2} a)}$

Step 1.4.2

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

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Step 1.4.2.1

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

$20 \sqrt[3]{27 (a^{2} a^{1})}$

Step 1.4.2.2

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

$20 \sqrt[3]{27 a^{2 + 1}}$

Step 1.4.3

Add $2$ and $1$ .

$20 \sqrt[3]{27 a^{3}}$

Step 2

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

$20 \sqrt[3]{{(3 a)}^{3}}$

Step 3

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

$20 (3 a)$

Step 4

Multiply $3$ by $20$ .

$60 a$