Precalculus Examples

$\sqrt[3]{8 x^{7}}$

Step 1

Rewrite $8 x^{7}$ as ${(2 x^{2})}^{3} x$ .

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Step 1.1

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

$\sqrt[3]{2^{3} x^{7}}$

Step 1.2

Factor out $x^{6}$ .

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

Step 1.3

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

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

Step 1.4

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

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

Step 2

Pull terms out from under the radical.

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