Question

1. what is the value of $2^0 + 2^{-1} + 2^{-2}$?

a. -6
b. $2^{-3}$
c. $1\frac{3}{4}$
d. 7

Explanation:

Step1: Evaluate each term separately

Recall rules: $a^0=1$, $a^{-n}=\frac{1}{a^n}$
$2^0 = 1$, $2^{-1}=\frac{1}{2}$, $2^{-2}=\frac{1}{4}$

Step2: Sum the calculated terms

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

Step3: Convert to common denominator

$\frac{4}{4} + \frac{2}{4} + \frac{1}{4} = \frac{4+2+1}{4} = \frac{7}{4} = 1\frac{3}{4}$

Answer:

C. $1\frac{3}{4}$