Basic Math Examples

$(- 5^{2}) + 9 (2 - 14 \div (- 4)) + (- 8) \sqrt{64 \cdot 16}$

Step 1

Simplify each term.

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Step 1.1

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

$- 1 \cdot 25 + 9 (2 - 14 \div (- 4)) + (- 8) \sqrt{64 \cdot 16}$

Step 1.2

Multiply $- 1$ by $25$ .

$- 25 + 9 (2 - 14 \div (- 4)) + (- 8) \sqrt{64 \cdot 16}$

Step 1.3

Simplify each term.

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Step 1.3.1

Rewrite the division as a fraction.

$- 25 + 9 (2 - \frac{14}{- 4}) + (- 8) \sqrt{64 \cdot 16}$

Step 1.3.2

Cancel the common factor of $14$ and $- 4$ .

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Step 1.3.2.1

Factor $2$ out of $14$ .

$- 25 + 9 (2 - \frac{2 (7)}{- 4}) + (- 8) \sqrt{64 \cdot 16}$

Step 1.3.2.2

Cancel the common factors.

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Step 1.3.2.2.1

Factor $2$ out of $- 4$ .

$- 25 + 9 (2 - \frac{2 \cdot 7}{2 \cdot - 2}) + (- 8) \sqrt{64 \cdot 16}$

Step 1.3.2.2.2

Cancel the common factor.

$- 25 + 9 (2 - \frac{2 \cdot 7}{2 \cdot - 2}) + (- 8) \sqrt{64 \cdot 16}$

Step 1.3.2.2.3

Rewrite the expression.

$- 25 + 9 (2 - \frac{7}{- 2}) + (- 8) \sqrt{64 \cdot 16}$

Step 1.3.3

Move the negative in front of the fraction.

$- 25 + 9 (2 - - \frac{7}{2}) + (- 8) \sqrt{64 \cdot 16}$

Step 1.3.4

Multiply $- - \frac{7}{2}$ .

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Step 1.3.4.1

Multiply $- 1$ by $- 1$ .

$- 25 + 9 (2 + 1 (\frac{7}{2})) + (- 8) \sqrt{64 \cdot 16}$

Step 1.3.4.2

Multiply $\frac{7}{2}$ by $1$ .

$- 25 + 9 (2 + \frac{7}{2}) + (- 8) \sqrt{64 \cdot 16}$

Step 1.4

To write $2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- 25 + 9 (2 \cdot \frac{2}{2} + \frac{7}{2}) + (- 8) \sqrt{64 \cdot 16}$

Step 1.5

Combine $2$ and $\frac{2}{2}$ .

$- 25 + 9 (\frac{2 \cdot 2}{2} + \frac{7}{2}) + (- 8) \sqrt{64 \cdot 16}$

Step 1.6

Combine the numerators over the common denominator.

$- 25 + 9 \frac{2 \cdot 2 + 7}{2} + (- 8) \sqrt{64 \cdot 16}$

Step 1.7

Simplify the numerator.

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Step 1.7.1

Multiply $2$ by $2$ .

$- 25 + 9 \frac{4 + 7}{2} + (- 8) \sqrt{64 \cdot 16}$

Step 1.7.2

Add $4$ and $7$ .

$- 25 + 9 (\frac{11}{2}) + (- 8) \sqrt{64 \cdot 16}$

Step 1.8

Multiply $9 (\frac{11}{2})$ .

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Step 1.8.1

Combine $9$ and $\frac{11}{2}$ .

$- 25 + \frac{9 \cdot 11}{2} + (- 8) \sqrt{64 \cdot 16}$

Step 1.8.2

Multiply $9$ by $11$ .

$- 25 + \frac{99}{2} + (- 8) \sqrt{64 \cdot 16}$

Step 1.9

Multiply $64$ by $16$ .

$- 25 + \frac{99}{2} - 8 \sqrt{1024}$

Step 1.10

Rewrite $1024$ as $32^{2}$ .

$- 25 + \frac{99}{2} - 8 \sqrt{32^{2}}$

Step 1.11

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

$- 25 + \frac{99}{2} - 8 \cdot 32$

Step 1.12

Multiply $- 8$ by $32$ .

$- 25 + \frac{99}{2} - 256$

Step 2

Find the common denominator.

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Step 2.1

Write $- 25$ as a fraction with denominator $1$ .

$\frac{- 25}{1} + \frac{99}{2} - 256$

Step 2.2

Multiply $\frac{- 25}{1}$ by $\frac{2}{2}$ .

$\frac{- 25}{1} \cdot \frac{2}{2} + \frac{99}{2} - 256$

Step 2.3

Multiply $\frac{- 25}{1}$ by $\frac{2}{2}$ .

$\frac{- 25 \cdot 2}{2} + \frac{99}{2} - 256$

Step 2.4

Write $- 256$ as a fraction with denominator $1$ .

$\frac{- 25 \cdot 2}{2} + \frac{99}{2} + \frac{- 256}{1}$

Step 2.5

Multiply $\frac{- 256}{1}$ by $\frac{2}{2}$ .

$\frac{- 25 \cdot 2}{2} + \frac{99}{2} + \frac{- 256}{1} \cdot \frac{2}{2}$

Step 2.6

Multiply $\frac{- 256}{1}$ by $\frac{2}{2}$ .

$\frac{- 25 \cdot 2}{2} + \frac{99}{2} + \frac{- 256 \cdot 2}{2}$

Step 3

Combine the numerators over the common denominator.

$\frac{- 25 \cdot 2 + 99 - 256 \cdot 2}{2}$

Step 4

Simplify each term.

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Step 4.1

Multiply $- 25$ by $2$ .

$\frac{- 50 + 99 - 256 \cdot 2}{2}$

Step 4.2

Multiply $- 256$ by $2$ .

$\frac{- 50 + 99 - 512}{2}$

Step 5

Simplify the expression.

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Step 5.1

Add $- 50$ and $99$ .

$\frac{49 - 512}{2}$

Step 5.2

Subtract $512$ from $49$ .

$\frac{- 463}{2}$

Step 5.3

Move the negative in front of the fraction.

$- \frac{463}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{463}{2}$

Decimal Form:

$- 231.5$

Mixed Number Form:

$- 231 \frac{1}{2}$