Algebra Examples

$10 - 8 \div 2 - 2^{2}$

Step 1

Find the common denominator.

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Step 1.1

Write $10$ as a fraction with denominator $1$ .

$\frac{10}{1} - 8 \div 2 - 2^{2}$

Step 1.2

Multiply $\frac{10}{1}$ by $\frac{2}{2}$ .

$\frac{10}{1} \cdot \frac{2}{2} - 8 \div 2 - 2^{2}$

Step 1.3

Multiply $\frac{10}{1}$ by $\frac{2}{2}$ .

$\frac{10 \cdot 2}{2} - 8 \div 2 - 2^{2}$

Step 1.4

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

$\frac{10 \cdot 2}{2} - 8 \div 2 + \frac{- 2^{2}}{1}$

Step 1.5

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

$\frac{10 \cdot 2}{2} - 8 \div 2 + \frac{- 2^{2}}{1} \cdot \frac{2}{2}$

Step 1.6

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

$\frac{10 \cdot 2}{2} - 8 \div 2 + \frac{- 2^{2} \cdot 2}{2}$

Step 2

Combine the numerators over the common denominator.

$\frac{10 \cdot 2 - 8 - 2^{2} \cdot 2}{2}$

Step 3

Simplify each term.

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Step 3.1

Multiply $10$ by $2$ .

$\frac{20 - 8 - 2^{2} \cdot 2}{2}$

Step 3.2

Multiply $2^{2}$ by $2$ by adding the exponents.

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Step 3.2.1

Move $2$ .

$\frac{20 - 8 - (2 \cdot 2^{2})}{2}$

Step 3.2.2

Multiply $2$ by $2^{2}$ .

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Step 3.2.2.1

Raise $2$ to the power of $1$ .

$\frac{20 - 8 - (2^{1} \cdot 2^{2})}{2}$

Step 3.2.2.2

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

$\frac{20 - 8 - 2^{1 + 2}}{2}$

Step 3.2.3

Add $1$ and $2$ .

$\frac{20 - 8 - 2^{3}}{2}$

Step 3.3

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

$\frac{20 - 8 - 1 \cdot 8}{2}$

Step 3.4

Multiply $- 1$ by $8$ .

$\frac{20 - 8 - 8}{2}$

Step 4

Simplify the expression.

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Step 4.1

Subtract $8$ from $20$ .

$\frac{12 - 8}{2}$

Step 4.2

Subtract $8$ from $12$ .

$\frac{4}{2}$

Step 4.3

Divide $4$ by $2$ .

$2$