Algebra Examples

$(\sqrt[3]{625 z}) (\sqrt[3]{162 z^{6}})$

Step 1

Rewrite $625 z$ as $5^{3} \cdot (5 z)$ .

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Step 1.1

Factor $125$ out of $625$ .

$\sqrt[3]{125 (5) z} \sqrt[3]{162 z^{6}}$

Step 1.2

Rewrite $125$ as $5^{3}$ .

$\sqrt[3]{5^{3} \cdot 5 z} \sqrt[3]{162 z^{6}}$

Step 1.3

Add parentheses.

$\sqrt[3]{5^{3} \cdot (5 z)} \sqrt[3]{162 z^{6}}$

Step 2

Pull terms out from under the radical.

$5 \sqrt[3]{5 z} \sqrt[3]{162 z^{6}}$

Step 3

Rewrite $162 z^{6}$ as ${(3 z^{2})}^{3} \cdot 6$ .

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Step 3.1

Factor $27$ out of $162$ .

$5 \sqrt[3]{5 z} \sqrt[3]{27 (6) z^{6}}$

Step 3.2

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

$5 \sqrt[3]{5 z} \sqrt[3]{3^{3} \cdot 6 z^{6}}$

Step 3.3

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

$5 \sqrt[3]{5 z} \sqrt[3]{3^{3} \cdot 6 {(z^{2})}^{3}}$

Step 3.4

Move $6$ .

$5 \sqrt[3]{5 z} \sqrt[3]{3^{3} {(z^{2})}^{3} \cdot 6}$

Step 3.5

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

$5 \sqrt[3]{5 z} \sqrt[3]{{(3 z^{2})}^{3} \cdot 6}$

Step 4

Pull terms out from under the radical.

$5 \sqrt[3]{5 z} (3 z^{2} \sqrt[3]{6})$

Step 5

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

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Step 5.1

Multiply $3$ by $5$ .

$15 \sqrt[3]{5 z} (z^{2} \sqrt[3]{6})$

Step 5.2

Combine using the product rule for radicals.

$15 (z^{2} \sqrt[3]{5 z \cdot 6})$

Step 5.3

Multiply $6$ by $5$ .

$15 (z^{2} \sqrt[3]{30 z})$

$15 z^{2} \sqrt[3]{30 z}$