Algebra Examples

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

Step 1

Remove parentheses.

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

Step 2

Simplify the numerator.

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

Multiply $- 4$ by $27$ .

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

Step 2.4

Subtract $108$ from $32$ .

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

Step 3

Simplify the denominator.

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Step 3.1

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

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

Step 3.2

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

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

Step 3.3

Multiply $- 1$ by $10$ .

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

Step 3.4

Add $7$ and $1$ .

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

Step 3.5

Subtract $10$ from $8$ .

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

Step 4

Divide $- 76$ by $- 2$ .

$38$