Evaluate ((2^5- square root of 400)/2)-(3(-5+1))

$(\frac{2^{5} - \sqrt{400}}{2}) - (3 (- 5 + 1))$

Step 1

Simplify each term.

Simplify the numerator.

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

$\frac{32 - \sqrt{400}}{2} - (3 (- 5 + 1))$

Rewrite $400$ as $20^{2}$ .

$\frac{32 - \sqrt{20^{2}}}{2} - (3 (- 5 + 1))$

Pull terms out from under the radical, assuming positive real numbers.

$\frac{32 - 1 \cdot 20}{2} - (3 (- 5 + 1))$

Multiply $- 1$ by $20$ .

$\frac{32 - 20}{2} - (3 (- 5 + 1))$

Subtract $20$ from $32$ .

$\frac{12}{2} - (3 (- 5 + 1))$

Divide $12$ by $2$ .

$6 - (3 (- 5 + 1))$

Add $- 5$ and $1$ .

$6 - (3 \cdot - 4)$

Multiply $- (3 \cdot - 4)$ .

Multiply $3$ by $- 4$ .

$6 - - 12$

Multiply $- 1$ by $- 12$ .

$6 + 12$

Step 2

Add $6$ and $12$ .

$18$