Algebra Examples

${(p^{- \frac{3}{4}} q^{3})}^{\frac{1}{3}}$

Step 1

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

${(\frac{1}{p^{\frac{3}{4}}} q^{3})}^{\frac{1}{3}}$

Step 2

Combine fractions.

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Step 2.1

Combine $\frac{1}{p^{\frac{3}{4}}}$ and $q^{3}$ .

${(\frac{q^{3}}{p^{\frac{3}{4}}})}^{\frac{1}{3}}$

Step 2.2

Apply the product rule to $\frac{q^{3}}{p^{\frac{3}{4}}}$ .

$\frac{{(q^{3})}^{\frac{1}{3}}}{{(p^{\frac{3}{4}})}^{\frac{1}{3}}}$

Step 3

Simplify the numerator.

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Step 3.1

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

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Step 3.1.1

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

$\frac{q^{3 (\frac{1}{3})}}{{(p^{\frac{3}{4}})}^{\frac{1}{3}}}$

Step 3.1.2

Cancel the common factor of $3$ .

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Step 3.1.2.1

Cancel the common factor.

$\frac{q^{3 (\frac{1}{3})}}{{(p^{\frac{3}{4}})}^{\frac{1}{3}}}$

Step 3.1.2.2

Rewrite the expression.

$\frac{q^{1}}{{(p^{\frac{3}{4}})}^{\frac{1}{3}}}$

Step 3.2

Simplify.

$\frac{q}{{(p^{\frac{3}{4}})}^{\frac{1}{3}}}$

Step 4

Multiply the exponents in ${(p^{\frac{3}{4}})}^{\frac{1}{3}}$ .

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Step 4.1

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

$\frac{q}{p^{\frac{3}{4} \cdot \frac{1}{3}}}$

Step 4.2

Cancel the common factor of $3$ .

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Step 4.2.1

Cancel the common factor.

$\frac{q}{p^{\frac{3}{4} \cdot \frac{1}{3}}}$

Step 4.2.2

Rewrite the expression.

$\frac{q}{p^{\frac{1}{4}}}$