Evaluate (4^2-8|7-9|)/(4(4-7)-30÷6)

$\frac{4^{2} - 8 | 7 - 9 |}{4 (4 - 7) - 30 \div 6}$

Cancel the common factor of $30$ and $6$ .

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Factor $6$ out of $30$ .

$\frac{4^{2} - 8 | 7 - 9 |}{4 (4 - 7) - \frac{6 \cdot 5}{6}}$

Cancel the common factors.

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Factor $6$ out of $6$ .

$\frac{4^{2} - 8 | 7 - 9 |}{4 (4 - 7) - \frac{6 \cdot 5}{6 (1)}}$

Cancel the common factor.

$\frac{4^{2} - 8 | 7 - 9 |}{4 (4 - 7) - \frac{6 \cdot 5}{6 \cdot 1}}$

Rewrite the expression.

$\frac{4^{2} - 8 | 7 - 9 |}{4 (4 - 7) - \frac{5}{1}}$

Divide $5$ by $1$ .

$\frac{4^{2} - 8 | 7 - 9 |}{4 (4 - 7) - 1 \cdot 5}$

Simplify the numerator.

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

$\frac{16 - 8 | 7 - 9 |}{4 (4 - 7) - 1 \cdot 5}$

Subtract $9$ from $7$ .

$\frac{16 - 8 | - 2 |}{4 (4 - 7) - 1 \cdot 5}$

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

$\frac{16 - 8 \cdot 2}{4 (4 - 7) - 1 \cdot 5}$

Multiply $- 8$ by $2$ .

$\frac{16 - 16}{4 (4 - 7) - 1 \cdot 5}$

Subtract $16$ from $16$ .

$\frac{0}{4 (4 - 7) - 1 \cdot 5}$

Simplify the denominator.

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Subtract $7$ from $4$ .

$\frac{0}{4 \cdot - 3 - 1 \cdot 5}$

Multiply $4$ by $- 3$ .

$\frac{0}{- 12 - 1 \cdot 5}$

Multiply $- 1$ by $5$ .

$\frac{0}{- 12 - 5}$

Subtract $5$ from $- 12$ .

$\frac{0}{- 17}$

Divide $0$ by $- 17$ .

$0$

Evaluate (4^2-8|7-9|)/(4(4-7)-30÷6)

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