Evaluate 2^1-2^-1+2^0

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

Step 1

Simplify each term.

Evaluate the exponent.

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

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

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

Anything raised to $0$ is $1$ .

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

Step 2

Find the common denominator.

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

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

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

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

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

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

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

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

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

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

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

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Simplify the expression.

Multiply $2$ by $2$ .

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

Subtract $1$ from $4$ .

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

Add $3$ and $2$ .

$\frac{5}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{2}$

Decimal Form:

$2.5$

Mixed Number Form:

$2 \frac{1}{2}$