Evaluate 3(2^-1-(-3/2))+2^0

$3 (2^{- 1} - (- \frac{3}{2})) + 2^{0}$

Step 1

Simplify each term.

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

$3 (\frac{1}{2} - (- \frac{3}{2})) + 2^{0}$

Multiply $- (- \frac{3}{2})$ .

Multiply $- 1$ by $- 1$ .

$3 (\frac{1}{2} + 1 (\frac{3}{2})) + 2^{0}$

Multiply $\frac{3}{2}$ by $1$ .

$3 (\frac{1}{2} + \frac{3}{2}) + 2^{0}$

Combine the numerators over the common denominator.

$3 \frac{1 + 3}{2} + 2^{0}$

Add $1$ and $3$ .

$3 (\frac{4}{2}) + 2^{0}$

Divide $4$ by $2$ .

$3 \cdot 2 + 2^{0}$

Multiply $3$ by $2$ .

$6 + 2^{0}$

Anything raised to $0$ is $1$ .

$6 + 1$

Step 2

Add $6$ and $1$ .

$7$