Precalculus Examples

$\sqrt[3]{27 a^{7} b^{3} c^{2}}$

Step 1

Rewrite $27 a^{7} b^{3} c^{2}$ as ${(3 a^{2} b)}^{3} (a c^{2})$ .

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Step 1.1

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

$\sqrt[3]{3^{3} a^{7} b^{3} c^{2}}$

Step 1.2

Factor out $a^{6}$ .

$\sqrt[3]{3^{3} (a^{6} a) b^{3} c^{2}}$

Step 1.3

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

$\sqrt[3]{3^{3} ({(a^{2})}^{3} a) b^{3} c^{2}}$

Step 1.4

Move $a$ .

$\sqrt[3]{3^{3} {(a^{2})}^{3} b^{3} a c^{2}}$

Step 1.5

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

$\sqrt[3]{{(3 a^{2} b)}^{3} a c^{2}}$

Step 1.6

Add parentheses.

$\sqrt[3]{{(3 a^{2} b)}^{3} (a c^{2})}$

Step 2

Pull terms out from under the radical.

$3 a^{2} b \sqrt[3]{a c^{2}}$