Algebra Examples

${(\frac{p^{1} q^{- 1}}{r^{- 2}})}^{- 4}$

Step 1

Move $q^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{p}{r^{- 2} q})}^{- 4}$

Step 2

Move $r^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{p r^{2}}{q})}^{- 4}$

Step 3

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

${(\frac{q}{p r^{2}})}^{4}$

Step 4

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

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Step 4.1

Apply the product rule to $\frac{q}{p r^{2}}$ .

$\frac{q^{4}}{{(p r^{2})}^{4}}$

Step 4.2

Apply the product rule to $p r^{2}$ .

$\frac{q^{4}}{p^{4} {(r^{2})}^{4}}$

Step 5

Multiply the exponents in ${(r^{2})}^{4}$ .

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Step 5.1

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

$\frac{q^{4}}{p^{4} r^{2 \cdot 4}}$

Step 5.2

Multiply $2$ by $4$ .

$\frac{q^{4}}{p^{4} r^{8}}$