Algebra Examples

$6 \sqrt[3]{25 a b^{2}} \cdot 5 \sqrt[3]{5 a^{2} b}$

Step 1

Multiply $6 \sqrt[3]{25 a b^{2}} (5 \sqrt[3]{5 a^{2} b})$ .

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Step 1.1

Multiply $5$ by $6$ .

$30 \sqrt[3]{25 a b^{2}} \sqrt[3]{5 a^{2} b}$

Step 1.2

Combine using the product rule for radicals.

$30 \sqrt[3]{5 a^{2} b (25 a b^{2})}$

Step 1.3

Multiply $25$ by $5$ .

$30 \sqrt[3]{125 a^{2} b (a b^{2})}$

Step 1.4

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

$30 \sqrt[3]{125 (a^{1} a^{2}) b \cdot b^{2}}$

Step 1.5

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

$30 \sqrt[3]{125 a^{1 + 2} b \cdot b^{2}}$

Step 1.6

Add $1$ and $2$ .

$30 \sqrt[3]{125 a^{3} b \cdot b^{2}}$

Step 1.7

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

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Step 1.7.1

Move $b^{2}$ .

$30 \sqrt[3]{125 a^{3} (b^{2} b)}$

Step 1.7.2

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

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Step 1.7.2.1

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

$30 \sqrt[3]{125 a^{3} (b^{2} b^{1})}$

Step 1.7.2.2

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

$30 \sqrt[3]{125 a^{3} b^{2 + 1}}$

Step 1.7.3

Add $2$ and $1$ .

$30 \sqrt[3]{125 a^{3} b^{3}}$

Step 2

Rewrite $125 a^{3} b^{3}$ as ${(5 a b)}^{3}$ .

$30 \sqrt[3]{{(5 a b)}^{3}}$

Step 3

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

$30 (5 a b)$

Step 4

Multiply $5$ by $30$ .

$150 a b$