Simplify 2^0+2^-1+2

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

Step 1

Simplify each term.

Anything raised to $0$ is $1$ .

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

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.

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

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

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

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

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

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

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

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

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

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

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.

Multiply $2$ by $2$ .

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

Add $2$ and $1$ .

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

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:

$3 \frac{1}{2}$