Precalculus Examples

$\sqrt[3]{x^{2} y^{6} z^{8}}$

Step 1

Rewrite $x^{2} y^{6} z^{8}$ as ${(y^{2} z^{2})}^{3} (x^{2} z^{2})$ .

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Step 1.1

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

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

Step 1.2

Factor out $z^{6}$ .

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

Step 1.3

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

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

Step 1.4

Move $x^{2}$ .

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

Step 1.5

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

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

Step 1.6

Add parentheses.

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

Step 2

Pull terms out from under the radical.

$y^{2} z^{2} \sqrt[3]{x^{2} z^{2}}$