Precalculus Examples

$\sqrt[3]{64 a^{9} b^{12} c^{- 3}}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\sqrt[3]{64 a^{9} b^{12} \frac{1}{c^{3}}}$

Step 2

Combine exponents.

Tap for more steps...

Step 2.1

Combine $64$ and $\frac{1}{c^{3}}$ .

$\sqrt[3]{a^{9} b^{12} \frac{64}{c^{3}}}$

Step 2.2

Combine $a^{9}$ and $\frac{64}{c^{3}}$ .

$\sqrt[3]{b^{12} \frac{a^{9} \cdot 64}{c^{3}}}$

Step 2.3

Combine $b^{12}$ and $\frac{a^{9} \cdot 64}{c^{3}}$ .

$\sqrt[3]{\frac{b^{12} (a^{9} \cdot 64)}{c^{3}}}$

Step 3

Remove unnecessary parentheses.

$\sqrt[3]{\frac{b^{12} a^{9} \cdot 64}{c^{3}}}$

Step 4

Move $64$ to the left of $b^{12} a^{9}$ .

$\sqrt[3]{\frac{64 \cdot (b^{12} a^{9})}{c^{3}}}$

Step 5

Rewrite $64 b^{12} a^{9}$ as ${(4 b^{4} a^{3})}^{3}$ .

$\sqrt[3]{\frac{{(4 b^{4} a^{3})}^{3}}{c^{3}}}$

Step 6

Rewrite $\frac{{(4 b^{4} a^{3})}^{3}}{c^{3}}$ as ${(\frac{4 b^{4} a^{3}}{c})}^{3}$ .

$\sqrt[3]{{(\frac{4 b^{4} a^{3}}{c})}^{3}}$

Step 7

Pull terms out from under the radical, assuming real numbers.

$\frac{4 b^{4} a^{3}}{c}$