Evaluate (-2-3)^3+3^-3(-4)

${(- 2 - 3)}^{3} + 3^{- 3} (- 4)$

Step 1

Simplify each term.

Subtract $3$ from $- 2$ .

${(- 5)}^{3} + 3^{- 3} (- 4)$

Raise $- 5$ to the power of $3$ .

$- 125 + 3^{- 3} (- 4)$

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

$- 125 + \frac{1}{3^{3}} \cdot - 4$

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

$- 125 + \frac{1}{27} \cdot - 4$

Combine $\frac{1}{27}$ and $- 4$ .

$- 125 + \frac{- 4}{27}$

Move the negative in front of the fraction.

$- 125 - \frac{4}{27}$

Step 2

To write $- 125$ as a fraction with a common denominator, multiply by $\frac{27}{27}$ .

$- 125 \cdot \frac{27}{27} - \frac{4}{27}$

Step 3

Combine $- 125$ and $\frac{27}{27}$ .

$\frac{- 125 \cdot 27}{27} - \frac{4}{27}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 125 \cdot 27 - 4}{27}$

Step 5

Simplify the numerator.

Multiply $- 125$ by $27$ .

$\frac{- 3375 - 4}{27}$

Subtract $4$ from $- 3375$ .

$\frac{- 3379}{27}$

Step 6

Move the negative in front of the fraction.

$- \frac{3379}{27}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{3379}{27}$

Decimal Form:

$- 125.\overline{148}$

Mixed Number Form:

$- 125 \frac{4}{27}$