Question

$2^{73} - 2^{72} - 2^{71}$ is the same as:

• A. $2^{69}$
• B. $2^{70}$
• C. $2^{71}$
• D. $2^{72}$

Hint:

When dealing with exponential expressions involving subtraction, always try factoring the smallest common power to simplify the expression.

Answer 1

The Correct Option is C

Step 1: Factor out lowest power All terms are powers of 2. Factor out the smallest power: \[ 2^{73} - 2^{72} - 2^{71} = 2^{71}(2^2 - 2^1 - 1) \] \[ = 2^{71}(4 - 2 - 1) = 2^{71} \cdot 1 = \boxed{2^{71}} \]