Precalculus Examples

${(u^{5} v^{9})}^{- \frac{1}{3}}$

Step 1

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

$\frac{1}{{(u^{5} v^{9})}^{\frac{1}{3}}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $u^{5} v^{9}$ .

$\frac{1}{{(u^{5})}^{\frac{1}{3}} {(v^{9})}^{\frac{1}{3}}}$

Step 2.2

Multiply the exponents in ${(u^{5})}^{\frac{1}{3}}$ .

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Step 2.2.1

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

$\frac{1}{u^{5 (\frac{1}{3})} {(v^{9})}^{\frac{1}{3}}}$

Step 2.2.2

Combine $5$ and $\frac{1}{3}$ .

$\frac{1}{u^{\frac{5}{3}} {(v^{9})}^{\frac{1}{3}}}$

Step 2.3

Multiply the exponents in ${(v^{9})}^{\frac{1}{3}}$ .

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Step 2.3.1

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

$\frac{1}{u^{\frac{5}{3}} v^{9 (\frac{1}{3})}}$

Step 2.3.2

Cancel the common factor of $3$ .

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Step 2.3.2.1

Factor $3$ out of $9$ .

$\frac{1}{u^{\frac{5}{3}} v^{3 (3) \frac{1}{3}}}$

Step 2.3.2.2

Cancel the common factor.

$\frac{1}{u^{\frac{5}{3}} v^{3 \cdot 3 \frac{1}{3}}}$

Step 2.3.2.3

Rewrite the expression.

$\frac{1}{u^{\frac{5}{3}} v^{3}}$

Step 3

Reorder factors in $\frac{1}{u^{\frac{5}{3}} v^{3}}$ .

$\frac{1}{v^{3} u^{\frac{5}{3}}}$