Find the Exact Value (-2)^-3-24

${(- 2)}^{- 3} - 24$

Step 1

Simplify each term.

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

$\frac{1}{{(- 2)}^{3}} - 24$

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

$\frac{1}{- 8} - 24$

Move the negative in front of the fraction.

$- \frac{1}{8} - 24$

Step 2

To write $- 24$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$- \frac{1}{8} - 24 \cdot \frac{8}{8}$

Step 3

Combine $- 24$ and $\frac{8}{8}$ .

$- \frac{1}{8} + \frac{- 24 \cdot 8}{8}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 1 - 24 \cdot 8}{8}$

Step 5

Simplify the numerator.

Multiply $- 24$ by $8$ .

$\frac{- 1 - 192}{8}$

Subtract $192$ from $- 1$ .

$\frac{- 193}{8}$

Step 6

Move the negative in front of the fraction.

$- \frac{193}{8}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{193}{8}$

Decimal Form:

$- 24.125$

Mixed Number Form:

$- 24 \frac{1}{8}$