Evaluate 31-(5-3*4)^2+(2^6)÷4

$31 - {(5 - 3 \cdot 4)}^{2} + 2^{6} \div 4$

Find the common denominator.

Write $31$ as a fraction with denominator $1$ .

$\frac{31}{1} - {(5 - 3 \cdot 4)}^{2} + 2^{6} \div 4$

Multiply $\frac{31}{1}$ by $\frac{4}{4}$ .

$\frac{31}{1} \cdot \frac{4}{4} - {(5 - 3 \cdot 4)}^{2} + 2^{6} \div 4$

Multiply $\frac{31}{1}$ by $\frac{4}{4}$ .

$\frac{31 \cdot 4}{4} - {(5 - 3 \cdot 4)}^{2} + 2^{6} \div 4$

Write $- {(5 - 3 \cdot 4)}^{2}$ as a fraction with denominator $1$ .

$\frac{31 \cdot 4}{4} + \frac{- {(5 - 3 \cdot 4)}^{2}}{1} + 2^{6} \div 4$

Multiply $\frac{- {(5 - 3 \cdot 4)}^{2}}{1}$ by $\frac{4}{4}$ .

$\frac{31 \cdot 4}{4} + \frac{- {(5 - 3 \cdot 4)}^{2}}{1} \cdot \frac{4}{4} + 2^{6} \div 4$

Multiply $\frac{- {(5 - 3 \cdot 4)}^{2}}{1}$ by $\frac{4}{4}$ .

$\frac{31 \cdot 4}{4} + \frac{- {(5 - 3 \cdot 4)}^{2} \cdot 4}{4} + 2^{6} \div 4$

Combine the numerators over the common denominator.

$\frac{31 \cdot 4 - {(5 - 3 \cdot 4)}^{2} \cdot 4 + 2^{6}}{4}$

Simplify each term.

Multiply $31$ by $4$ .

$\frac{124 - {(5 - 3 \cdot 4)}^{2} \cdot 4 + 2^{6}}{4}$

Multiply $- 3$ by $4$ .

$\frac{124 - {(5 - 12)}^{2} \cdot 4 + 2^{6}}{4}$

Subtract $12$ from $5$ .

$\frac{124 - {(- 7)}^{2} \cdot 4 + 2^{6}}{4}$

Raise $- 7$ to the power of $2$ .

$\frac{124 - 1 \cdot 49 \cdot 4 + 2^{6}}{4}$

Multiply $- 1$ by $49$ .

$\frac{124 - 49 \cdot 4 + 2^{6}}{4}$

Multiply $- 49$ by $4$ .

$\frac{124 - 196 + 2^{6}}{4}$

Raise $2$ to the power of $6$ .

$\frac{124 - 196 + 64}{4}$

Simplify the expression.

Subtract $196$ from $124$ .

$\frac{- 72 + 64}{4}$

Add $- 72$ and $64$ .

$\frac{- 8}{4}$

Divide $- 8$ by $4$ .

$- 2$