Precalculus Examples

${(\frac{q^{- 1} r^{- 1} s^{- 5}}{r^{- 3} s q^{- 7}})}^{- 1}$

Step 1

Move $s^{- 5}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{q^{- 1} r^{- 1}}{r^{- 3} s q^{- 7} s^{5}})}^{- 1}$

Step 2

Multiply $s$ by $s^{5}$ by adding the exponents.

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Step 2.1

Move $s^{5}$ .

${(\frac{q^{- 1} r^{- 1}}{r^{- 3} (s^{5} s) q^{- 7}})}^{- 1}$

Step 2.2

Multiply $s^{5}$ by $s$ .

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Step 2.2.1

Raise $s$ to the power of $1$ .

${(\frac{q^{- 1} r^{- 1}}{r^{- 3} (s^{5} s^{1}) q^{- 7}})}^{- 1}$

Step 2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(\frac{q^{- 1} r^{- 1}}{r^{- 3} s^{5 + 1} q^{- 7}})}^{- 1}$

Step 2.3

Add $5$ and $1$ .

${(\frac{q^{- 1} r^{- 1}}{r^{- 3} s^{6} q^{- 7}})}^{- 1}$

Step 3

Move $q^{- 7}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{q^{- 1} r^{- 1} q^{7}}{r^{- 3} s^{6}})}^{- 1}$

Step 4

Move $r^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{q^{- 1} r^{- 1} q^{7} r^{3}}{s^{6}})}^{- 1}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $q^{- 1}$ by $q^{7}$ by adding the exponents.

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Step 5.1.1

Move $q^{7}$ .

${(\frac{q^{7} q^{- 1} r^{- 1} r^{3}}{s^{6}})}^{- 1}$

Step 5.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(\frac{q^{7 - 1} r^{- 1} r^{3}}{s^{6}})}^{- 1}$

Step 5.1.3

Subtract $1$ from $7$ .

${(\frac{q^{6} r^{- 1} r^{3}}{s^{6}})}^{- 1}$

Step 5.2

Multiply $r^{- 1}$ by $r^{3}$ by adding the exponents.

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Step 5.2.1

Move $r^{3}$ .

${(\frac{q^{6} (r^{3} r^{- 1})}{s^{6}})}^{- 1}$

Step 5.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(\frac{q^{6} r^{3 - 1}}{s^{6}})}^{- 1}$

Step 5.2.3

Subtract $1$ from $3$ .

${(\frac{q^{6} r^{2}}{s^{6}})}^{- 1}$

Step 6

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

$\frac{s^{6}}{q^{6} r^{2}}$