Evaluate (7+|-8-5^2|)/((1-4)^3+17)

$\frac{7 + | - 8 - 5^{2} |}{{(1 - 4)}^{3} + 17}$

Simplify the numerator.

Simplify each term.

Raise $5$ to the power of $2$ .

$\frac{7 + | - 8 - 1 \cdot 25 |}{{(1 - 4)}^{3} + 17}$

Multiply $- 1$ by $25$ .

$\frac{7 + | - 8 - 25 |}{{(1 - 4)}^{3} + 17}$

Subtract $25$ from $- 8$ .

$\frac{7 + | - 33 |}{{(1 - 4)}^{3} + 17}$

The absolute value is the distance between a number and zero. The distance between $- 33$ and $0$ is $33$ .

$\frac{7 + 33}{{(1 - 4)}^{3} + 17}$

Add $7$ and $33$ .

$\frac{40}{{(1 - 4)}^{3} + 17}$

Simplify the denominator.

Subtract $4$ from $1$ .

$\frac{40}{{(- 3)}^{3} + 17}$

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

$\frac{40}{- 27 + 17}$

Add $- 27$ and $17$ .

$\frac{40}{- 10}$

Divide $40$ by $- 10$ .

$- 4$