Simplify: \(\frac{1}{4}(2^n - 2^{n + 2}\))
A
\(2^{n - 2} - 2^n\)
B
\(2^{n-2}(1-2^n\))
C
\(2^n + 2^{2 + n}\)
D
\(2^{2n}\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
\(\frac{1}{4}(2^n - 2^{n + 2}\)) = \(\frac{1}{4}(2^n - 2^n \times2^2\))
\(\frac{1}{4} \times2^n(1 - 2^2\)) = \(2^{-2}\times2^n(1 - 2^2\))
\(2^{n - 2}(2^0 - 2^2\)) = \(2^{n - 2} - 2^n\)
Source: Myschool Past Questions Archive (Record #22873)