Algebra Examples

$2^{0} + 2^{- 1} + 2$

Step 1

Simplify each term.

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Step 1.1

Anything raised to $0$ is $1$ .

$1 + 2^{- 1} + 2$

Step 1.2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$1 + \frac{1}{2} + 2$

Step 2

Find the common denominator.

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Step 2.1

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

$\frac{1}{1} + \frac{1}{2} + 2$

Step 2.2

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

$\frac{1}{1} \cdot \frac{2}{2} + \frac{1}{2} + 2$

Step 2.3

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

$\frac{2}{2} + \frac{1}{2} + 2$

Step 2.4

Write $2$ as a fraction with denominator $1$ .

$\frac{2}{2} + \frac{1}{2} + \frac{2}{1}$

Step 2.5

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

$\frac{2}{2} + \frac{1}{2} + \frac{2}{1} \cdot \frac{2}{2}$

Step 2.6

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

$\frac{2}{2} + \frac{1}{2} + \frac{2 \cdot 2}{2}$

Step 3

Combine the numerators over the common denominator.

$\frac{2 + 1 + 2 \cdot 2}{2}$

Step 4

Simplify the expression.

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Step 4.1

Multiply $2$ by $2$ .

$\frac{2 + 1 + 4}{2}$

Step 4.2

Add $2$ and $1$ .

$\frac{3 + 4}{2}$

Step 4.3

Add $3$ and $4$ .

$\frac{7}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{2}$

Decimal Form:

$3.5$

Mixed Number Form:

$3 \frac{1}{2}$