Algebra Examples

$(\sqrt[3]{80 z}) (\sqrt[3]{15 z^{8}})$

Step 1

Rewrite $80 z$ as $2^{3} \cdot (10 z)$ .

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Step 1.1

Factor $8$ out of $80$ .

$\sqrt[3]{8 (10) z} \sqrt[3]{15 z^{8}}$

Step 1.2

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

$\sqrt[3]{2^{3} \cdot 10 z} \sqrt[3]{15 z^{8}}$

Step 1.3

Add parentheses.

$\sqrt[3]{2^{3} \cdot (10 z)} \sqrt[3]{15 z^{8}}$

Step 2

Pull terms out from under the radical.

$2 \sqrt[3]{10 z} \sqrt[3]{15 z^{8}}$

Step 3

Rewrite $15 z^{8}$ as ${(z^{2})}^{3} \cdot (15 z^{2})$ .

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Step 3.1

Factor out $z^{6}$ .

$2 \sqrt[3]{10 z} \sqrt[3]{15 (z^{6} z^{2})}$

Step 3.2

Rewrite $z^{6}$ as ${(z^{2})}^{3}$ .

$2 \sqrt[3]{10 z} \sqrt[3]{15 ({(z^{2})}^{3} z^{2})}$

Step 3.3

Reorder $15$ and ${(z^{2})}^{3}$ .

$2 \sqrt[3]{10 z} \sqrt[3]{{(z^{2})}^{3} \cdot 15 z^{2}}$

Step 3.4

Add parentheses.

$2 \sqrt[3]{10 z} \sqrt[3]{{(z^{2})}^{3} \cdot (15 z^{2})}$

Step 4

Pull terms out from under the radical.

$2 \sqrt[3]{10 z} (z^{2} \sqrt[3]{15 z^{2}})$

Step 5

Multiply $2 \sqrt[3]{10 z} (z^{2} \sqrt[3]{15 z^{2}})$ .

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Step 5.1

Combine using the product rule for radicals.

$2 (z^{2} \sqrt[3]{10 z (15 z^{2})})$

Step 5.2

Multiply $15$ by $10$ .

$2 (z^{2} \sqrt[3]{150 z \cdot z^{2}})$

Step 5.3

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

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Step 5.3.1

Move $z^{2}$ .

$2 (z^{2} \sqrt[3]{150 (z^{2} z)})$

Step 5.3.2

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

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Step 5.3.2.1

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

$2 (z^{2} \sqrt[3]{150 (z^{2} z^{1})})$

Step 5.3.2.2

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

$2 (z^{2} \sqrt[3]{150 z^{2 + 1}})$

Step 5.3.3

Add $2$ and $1$ .

$2 (z^{2} \sqrt[3]{150 z^{3}})$

Step 6

Reorder $150$ and $z^{3}$ .

$2 (z^{2} \sqrt[3]{z^{3} \cdot 150})$

Step 7

Pull terms out from under the radical.

$2 (z^{2} (z \sqrt[3]{150}))$

Step 8

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

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Step 8.1

Move $z$ .

$2 (z \cdot z^{2} \sqrt[3]{150})$

Step 8.2

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

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Step 8.2.1

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

$2 (z^{1} z^{2} \sqrt[3]{150})$

Step 8.2.2

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

$2 (z^{1 + 2} \sqrt[3]{150})$

Step 8.3

Add $1$ and $2$ .

$2 (z^{3} \sqrt[3]{150})$

$2 z^{3} \sqrt[3]{150}$