Algebra Examples

$(\sqrt[3]{135 h^{2}}) (\sqrt[3]{4 h^{2}})$

Step 1

Rewrite $135 h^{2}$ as $3^{3} \cdot (5 h^{2})$ .

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Step 1.1

Factor $27$ out of $135$ .

$\sqrt[3]{27 (5) h^{2}} \sqrt[3]{4 h^{2}}$

Step 1.2

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

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

Step 1.3

Add parentheses.

$\sqrt[3]{3^{3} \cdot (5 h^{2})} \sqrt[3]{4 h^{2}}$

Step 2

Pull terms out from under the radical.

$3 \sqrt[3]{5 h^{2}} \sqrt[3]{4 h^{2}}$

Step 3

Multiply $3 \sqrt[3]{5 h^{2}} \sqrt[3]{4 h^{2}}$ .

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Step 3.1

Combine using the product rule for radicals.

$3 \sqrt[3]{4 h^{2} (5 h^{2})}$

Step 3.2

Multiply $5$ by $4$ .

$3 \sqrt[3]{20 h^{2} h^{2}}$

Step 3.3

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

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Step 3.3.1

Move $h^{2}$ .

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

Step 3.3.2

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

$3 \sqrt[3]{20 h^{2 + 2}}$

Step 3.3.3

Add $2$ and $2$ .

$3 \sqrt[3]{20 h^{4}}$

Step 4

Rewrite $20 h^{4}$ as $h^{3} \cdot (20 h)$ .

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Step 4.1

Factor out $h^{3}$ .

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

Step 4.2

Reorder $20$ and $h^{3}$ .

$3 \sqrt[3]{h^{3} \cdot 20 h}$

Step 4.3

Add parentheses.

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

Step 5

Pull terms out from under the radical.

$3 h \sqrt[3]{20 h}$