Evaluate ((4-8)^2-3|5-7|)/(40-5*4^2)

$\frac{{(4 - 8)}^{2} - 3 | 5 - 7 |}{40 - 5 \cdot 4^{2}}$

Step 1

Simplify the numerator.

Subtract $8$ from $4$ .

$\frac{{(- 4)}^{2} - 3 | 5 - 7 |}{40 - 5 \cdot 4^{2}}$

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

$\frac{16 - 3 | 5 - 7 |}{40 - 5 \cdot 4^{2}}$

Subtract $7$ from $5$ .

$\frac{16 - 3 | - 2 |}{40 - 5 \cdot 4^{2}}$

The absolute value is the distance between a number and zero. The distance between $- 2$ and $0$ is $2$ .

$\frac{16 - 3 \cdot 2}{40 - 5 \cdot 4^{2}}$

Multiply $- 3$ by $2$ .

$\frac{16 - 6}{40 - 5 \cdot 4^{2}}$

Subtract $6$ from $16$ .

$\frac{10}{40 - 5 \cdot 4^{2}}$

Step 2

Simplify the denominator.

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

$\frac{10}{40 - 5 \cdot 16}$

Multiply $- 5$ by $16$ .

$\frac{10}{40 - 80}$

Subtract $80$ from $40$ .

$\frac{10}{- 40}$

Step 3

Reduce the expression by cancelling the common factors.

Cancel the common factor of $10$ and $- 40$ .

Factor $10$ out of $10$ .

$\frac{10 (1)}{- 40}$

Cancel the common factors.

Factor $10$ out of $- 40$ .

$\frac{10 \cdot 1}{10 \cdot - 4}$

Cancel the common factor.

$\frac{10 \cdot 1}{10 \cdot - 4}$

Rewrite the expression.

$\frac{1}{- 4}$

Move the negative in front of the fraction.

$- \frac{1}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{4}$

Decimal Form:

$- 0.25$