Algebra Examples

$(\sqrt[3]{16 z^{6}}) (\sqrt[3]{6 z})$

Step 1

Rewrite $16 z^{6}$ as ${(2 z^{2})}^{3} \cdot 2$ .

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Step 1.1

Factor $8$ out of $16$ .

$\sqrt[3]{8 (2) z^{6}} \sqrt[3]{6 z}$

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

Move $2$ .

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

Step 1.5

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

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Step 3.1

Combine using the product rule for radicals.

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

Step 3.2

Multiply $2$ by $6$ .

$2 z^{2} \sqrt[3]{12 z}$