Precalculus Examples

${(\frac{p^{3}}{5 q^{3}})}^{- 4}$

Step 1

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{5 q^{3}}{p^{3}})}^{4}$

Step 2

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 2.1

Apply the product rule to $\frac{5 q^{3}}{p^{3}}$ .

$\frac{{(5 q^{3})}^{4}}{{(p^{3})}^{4}}$

Step 2.2

Apply the product rule to $5 q^{3}$ .

$\frac{5^{4} {(q^{3})}^{4}}{{(p^{3})}^{4}}$

Step 3

Simplify the numerator.

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Step 3.1

Raise $5$ to the power of $4$ .

$\frac{625 {(q^{3})}^{4}}{{(p^{3})}^{4}}$

Step 3.2

Multiply the exponents in ${(q^{3})}^{4}$ .

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Step 3.2.1

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

$\frac{625 q^{3 \cdot 4}}{{(p^{3})}^{4}}$

Step 3.2.2

Multiply $3$ by $4$ .

$\frac{625 q^{12}}{{(p^{3})}^{4}}$

Step 4

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

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Step 4.1

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

$\frac{625 q^{12}}{p^{3 \cdot 4}}$

Step 4.2

Multiply $3$ by $4$ .

$\frac{625 q^{12}}{p^{12}}$