Evaluate (-(8-11)^3-3|-14|)/(2^4-7)

$\frac{- {(8 - 11)}^{3} - 3 | - 14 |}{2^{4} - 7}$

Simplify the numerator.

Subtract $11$ from $8$ .

$\frac{- {(- 3)}^{3} - 3 | - 14 |}{2^{4} - 7}$

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

$\frac{- - 27 - 3 | - 14 |}{2^{4} - 7}$

Multiply $- 1$ by $- 27$ .

$\frac{27 - 3 | - 14 |}{2^{4} - 7}$

The absolute value is the distance between a number and zero. The distance between $- 14$ and $0$ is $14$ .

$\frac{27 - 3 \cdot 14}{2^{4} - 7}$

Multiply $- 3$ by $14$ .

$\frac{27 - 42}{2^{4} - 7}$

Subtract $42$ from $27$ .

$\frac{- 15}{2^{4} - 7}$

Simplify the denominator.

Raise $2$ to the power of $4$ .

$\frac{- 15}{16 - 7}$

Subtract $7$ from $16$ .

$\frac{- 15}{9}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $- 15$ and $9$ .

Factor $3$ out of $- 15$ .

$\frac{3 (- 5)}{9}$

Cancel the common factors.

Factor $3$ out of $9$ .

$\frac{3 \cdot - 5}{3 \cdot 3}$

Cancel the common factor.

$\frac{3 \cdot - 5}{3 \cdot 3}$

Rewrite the expression.

$\frac{- 5}{3}$

Move the negative in front of the fraction.

$- \frac{5}{3}$

The result can be shown in multiple forms.

Exact Form:

$- \frac{5}{3}$

Decimal Form:

$- 1.\overline{6}$

Mixed Number Form:

$- 1 \frac{2}{3}$