Simplify \(\frac{3^n - 3^{n - 1}}{3^3 \times 3^n - 27 \times 3^{n - 1}}\)
A
1
B
6
C
\(\frac{1}{27}\)
D
\(\frac{4}{3}\)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
\(\frac{3^n - 3^{n - 1}}{3^3 \times 3^n - 27 \times 3^{n - 1}}\) = \(\frac{3^n - 3^{n - 1}}{3^3(3^n - 3^{n - 1})}\)
= \(\frac{3^n - 3^{n - 1}}{27(3^n - 3^{n - 1})}\)
= \(\frac{1}{27}\)
Source: Myschool Past Questions Archive (Record #32346)