Simplify (2^5-4*3^3)/(7+(1- square root of 100))

$\frac{2^{5} - 4 \cdot 3^{3}}{7 + (1 - \sqrt{100})}$

Step 1

Remove parentheses.

$\frac{2^{5} - 4 \cdot 3^{3}}{7 + 1 - \sqrt{100}}$

Step 2

Simplify the numerator.

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

$\frac{32 - 4 \cdot 3^{3}}{7 + 1 - \sqrt{100}}$

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

$\frac{32 - 4 \cdot 27}{7 + 1 - \sqrt{100}}$

Multiply $- 4$ by $27$ .

$\frac{32 - 108}{7 + 1 - \sqrt{100}}$

Subtract $108$ from $32$ .

$\frac{- 76}{7 + 1 - \sqrt{100}}$

Step 3

Simplify the denominator.

Rewrite $100$ as $10^{2}$ .

$\frac{- 76}{7 + 1 - \sqrt{10^{2}}}$

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

$\frac{- 76}{7 + 1 - 1 \cdot 10}$

Multiply $- 1$ by $10$ .

$\frac{- 76}{7 + 1 - 10}$

Add $7$ and $1$ .

$\frac{- 76}{8 - 10}$

Subtract $10$ from $8$ .

$\frac{- 76}{- 2}$

Step 4

Divide $- 76$ by $- 2$ .

$38$