Precalculus Examples

$\sqrt[3]{512 x^{5} a^{6}}$

Step 1

Rewrite $512 x^{5} a^{6}$ as ${(8 x a^{2})}^{3} x^{2}$ .

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Step 1.1

Rewrite $512$ as $8^{3}$ .

$\sqrt[3]{8^{3} x^{5} a^{6}}$

Step 1.2

Factor out $x^{3}$ .

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

Step 1.3

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

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

Step 1.4

Move $x^{2}$ .

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

Step 1.5

Rewrite $8^{3} (x^{3}) {(a^{2})}^{3}$ as ${(8 x a^{2})}^{3}$ .

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

Step 2

Pull terms out from under the radical.

$8 x a^{2} \sqrt[3]{x^{2}}$