Evaluate Using the Given Value (-m)^-3n if m=2 and n=-24

${(- m)}^{- 3} n$ if $m = 2$ and $n = - 24$

Step 1

Replace the variable $m$ with $2$ in the expression.

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

Step 2

Replace the variable $n$ with $- 24$ in the expression.

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

Step 3

Multiply $- 1$ by $2$ .

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

Step 4

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

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

Step 5

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

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

Step 6

Cancel the common factor of $8$ .

Factor $8$ out of $- 8$ .

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

Factor $8$ out of $- 24$ .

$\frac{1}{8 \cdot - 1} \cdot (8 \cdot - 3)$

Cancel the common factor.

$\frac{1}{8 \cdot - 1} \cdot (8 \cdot - 3)$

Rewrite the expression.

$\frac{1}{- 1} \cdot - 3$

Step 7

Combine $\frac{1}{- 1}$ and $- 3$ .

$\frac{- 3}{- 1}$

Step 8

Divide $- 3$ by $- 1$ .

$3$