Basic Math Examples

$- {(- 2)}^{3} + {(- 1)}^{0} - \sqrt{25 - 3^{2}} - 5^{3} \div 25$

Step 1

Find the common denominator.

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Step 1.1

Write $- {(- 2)}^{3}$ as a fraction with denominator $1$ .

$\frac{- {(- 2)}^{3}}{1} + {(- 1)}^{0} - \sqrt{25 - 3^{2}} - 5^{3} \div 25$

Step 1.2

Multiply $\frac{- {(- 2)}^{3}}{1}$ by $\frac{25}{25}$ .

$\frac{- {(- 2)}^{3}}{1} \cdot \frac{25}{25} + {(- 1)}^{0} - \sqrt{25 - 3^{2}} - 5^{3} \div 25$

Step 1.3

Multiply $\frac{- {(- 2)}^{3}}{1}$ by $\frac{25}{25}$ .

$\frac{- {(- 2)}^{3} \cdot 25}{25} + {(- 1)}^{0} - \sqrt{25 - 3^{2}} - 5^{3} \div 25$

Step 1.4

Write ${(- 1)}^{0}$ as a fraction with denominator $1$ .

$\frac{- {(- 2)}^{3} \cdot 25}{25} + \frac{{(- 1)}^{0}}{1} - \sqrt{25 - 3^{2}} - 5^{3} \div 25$

Step 1.5

Multiply $\frac{{(- 1)}^{0}}{1}$ by $\frac{25}{25}$ .

$\frac{- {(- 2)}^{3} \cdot 25}{25} + \frac{{(- 1)}^{0}}{1} \cdot \frac{25}{25} - \sqrt{25 - 3^{2}} - 5^{3} \div 25$

Step 1.6

Multiply $\frac{{(- 1)}^{0}}{1}$ by $\frac{25}{25}$ .

$\frac{- {(- 2)}^{3} \cdot 25}{25} + \frac{{(- 1)}^{0} \cdot 25}{25} - \sqrt{25 - 3^{2}} - 5^{3} \div 25$

Step 1.7

Write $- \sqrt{25 - 3^{2}}$ as a fraction with denominator $1$ .

$\frac{- {(- 2)}^{3} \cdot 25}{25} + \frac{{(- 1)}^{0} \cdot 25}{25} + \frac{- \sqrt{25 - 3^{2}}}{1} - 5^{3} \div 25$

Step 1.8

Multiply $\frac{- \sqrt{25 - 3^{2}}}{1}$ by $\frac{25}{25}$ .

$\frac{- {(- 2)}^{3} \cdot 25}{25} + \frac{{(- 1)}^{0} \cdot 25}{25} + \frac{- \sqrt{25 - 3^{2}}}{1} \cdot \frac{25}{25} - 5^{3} \div 25$

Step 1.9

Multiply $\frac{- \sqrt{25 - 3^{2}}}{1}$ by $\frac{25}{25}$ .

$\frac{- {(- 2)}^{3} \cdot 25}{25} + \frac{{(- 1)}^{0} \cdot 25}{25} + \frac{- \sqrt{25 - 3^{2}} \cdot 25}{25} - 5^{3} \div 25$

Step 2

Combine the numerators over the common denominator.

$\frac{- {(- 2)}^{3} \cdot 25 + {(- 1)}^{0} \cdot 25 - \sqrt{25 - 3^{2}} \cdot 25 - 5^{3}}{25}$

Step 3

Simplify each term.

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Step 3.1

Raise $- 2$ to the power of $3$ .

$\frac{- - 8 \cdot 25 + {(- 1)}^{0} \cdot 25 - \sqrt{25 - 3^{2}} \cdot 25 - 5^{3}}{25}$

Step 3.2

Multiply $- - 8 \cdot 25$ .

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Step 3.2.1

Multiply $- 1$ by $- 8$ .

$\frac{8 \cdot 25 + {(- 1)}^{0} \cdot 25 - \sqrt{25 - 3^{2}} \cdot 25 - 5^{3}}{25}$

Step 3.2.2

Multiply $8$ by $25$ .

$\frac{200 + {(- 1)}^{0} \cdot 25 - \sqrt{25 - 3^{2}} \cdot 25 - 5^{3}}{25}$

Step 3.3

Anything raised to $0$ is $1$ .

$\frac{200 + 1 \cdot 25 - \sqrt{25 - 3^{2}} \cdot 25 - 5^{3}}{25}$

Step 3.4

Multiply $25$ by $1$ .

$\frac{200 + 25 - \sqrt{25 - 3^{2}} \cdot 25 - 5^{3}}{25}$

Step 3.5

Raise $3$ to the power of $2$ .

$\frac{200 + 25 - \sqrt{25 - 1 \cdot 9} \cdot 25 - 5^{3}}{25}$

Step 3.6

Multiply $- 1$ by $9$ .

$\frac{200 + 25 - \sqrt{25 - 9} \cdot 25 - 5^{3}}{25}$

Step 3.7

Subtract $9$ from $25$ .

$\frac{200 + 25 - \sqrt{16} \cdot 25 - 5^{3}}{25}$

Step 3.8

Rewrite $16$ as $4^{2}$ .

$\frac{200 + 25 - \sqrt{4^{2}} \cdot 25 - 5^{3}}{25}$

Step 3.9

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

$\frac{200 + 25 - 1 \cdot 4 \cdot 25 - 5^{3}}{25}$

Step 3.10

Multiply $- 1 \cdot 4 \cdot 25$ .

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Step 3.10.1

Multiply $- 1$ by $4$ .

$\frac{200 + 25 - 4 \cdot 25 - 5^{3}}{25}$

Step 3.10.2

Multiply $- 4$ by $25$ .

$\frac{200 + 25 - 100 - 5^{3}}{25}$

Step 3.11

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

$\frac{200 + 25 - 100 - 1 \cdot 125}{25}$

Step 3.12

Multiply $- 1$ by $125$ .

$\frac{200 + 25 - 100 - 125}{25}$

Step 4

Simplify the expression.

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Step 4.1

Add $200$ and $25$ .

$\frac{225 - 100 - 125}{25}$

Step 4.2

Subtract $100$ from $225$ .

$\frac{125 - 125}{25}$

Step 4.3

Subtract $125$ from $125$ .

$\frac{0}{25}$

Step 4.4

Divide $0$ by $25$ .

$0$