Precalculus Examples

${(c^{2} d^{3})}^{- \frac{1}{3}}$

Step 1

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

$\frac{1}{{(c^{2} d^{3})}^{\frac{1}{3}}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $c^{2} d^{3}$ .

$\frac{1}{{(c^{2})}^{\frac{1}{3}} {(d^{3})}^{\frac{1}{3}}}$

Step 2.2

Multiply the exponents in ${(c^{2})}^{\frac{1}{3}}$ .

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Step 2.2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{1}{c^{2 (\frac{1}{3})} {(d^{3})}^{\frac{1}{3}}}$

Step 2.2.2

Combine $2$ and $\frac{1}{3}$ .

$\frac{1}{c^{\frac{2}{3}} {(d^{3})}^{\frac{1}{3}}}$

Step 2.3

Multiply the exponents in ${(d^{3})}^{\frac{1}{3}}$ .

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Step 2.3.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{1}{c^{\frac{2}{3}} d^{3 (\frac{1}{3})}}$

Step 2.3.2

Cancel the common factor of $3$ .

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Step 2.3.2.1

Cancel the common factor.

$\frac{1}{c^{\frac{2}{3}} d^{3 (\frac{1}{3})}}$

Step 2.3.2.2

Rewrite the expression.

$\frac{1}{c^{\frac{2}{3}} d^{1}}$

Step 2.4

Simplify.

$\frac{1}{c^{\frac{2}{3}} d}$

Step 3

Reorder factors in $\frac{1}{c^{\frac{2}{3}} d}$ .

$\frac{1}{d c^{\frac{2}{3}}}$