Precalculus Examples

${(- 2 x^{- 1})}^{- 3}$

Step 1

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

${(- 2 \frac{1}{x})}^{- 3}$

Step 2

Combine $- 2$ and $\frac{1}{x}$ .

${(\frac{- 2}{x})}^{- 3}$

Step 3

Move the negative in front of the fraction.

${(- \frac{2}{x})}^{- 3}$

Step 4

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

${(- \frac{x}{2})}^{3}$

Step 5

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

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Step 5.1

Apply the product rule to $- \frac{x}{2}$ .

${(- 1)}^{3} {(\frac{x}{2})}^{3}$

Step 5.2

Apply the product rule to $\frac{x}{2}$ .

${(- 1)}^{3} \frac{x^{3}}{2^{3}}$

Step 6

Raise $- 1$ to the power of $3$ .

$- \frac{x^{3}}{2^{3}}$

Step 7

Raise $2$ to the power of $3$ .

$- \frac{x^{3}}{8}$