Pre-Algebra Examples

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

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $4$ as $2^{2}$ .

$\frac{(- 7 + \sqrt{2^{2}}) (- 5^{2})}{- 2 - 3}$

Step 1.2

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

$\frac{(- 7 + 2) (- 5^{2})}{- 2 - 3}$

Step 1.3

Add $- 7$ and $2$ .

$\frac{- 5 \cdot - 1 \cdot 5^{2}}{- 2 - 3}$

Step 1.4

Combine exponents.

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Step 1.4.1

Factor out negative.

$\frac{- (- 5 \cdot 5^{2})}{- 2 - 3}$

Step 1.4.2

Factor out negative.

$\frac{- - (5 \cdot 5^{2})}{- 2 - 3}$

Step 1.4.3

Raise $5$ to the power of $1$ .

$\frac{- - (5^{1} \cdot 5^{2})}{- 2 - 3}$

Step 1.4.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{- - 5^{1 + 2}}{- 2 - 3}$

Step 1.4.5

Add $1$ and $2$ .

$\frac{- - 5^{3}}{- 2 - 3}$

Step 1.4.6

Multiply $- 1$ by $- 1$ .

$\frac{1 \cdot 5^{3}}{- 2 - 3}$

Step 1.4.7

Multiply $5^{3}$ by $1$ .

$\frac{5^{3}}{- 2 - 3}$

Step 1.5

Raise $5$ to the power of $3$ .

$\frac{125}{- 2 - 3}$

Step 2

Subtract $3$ from $- 2$ .

$\frac{125}{- 5}$

Step 3

Divide $125$ by $- 5$ .

$- 25$