Simplify; \(\frac{3^{n - 1} \times 27^{n + 1}}{81^{n}}\)
A
32n
B
9
C
3n
D
3n + 1
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
\(\frac{3^{n - 1} \times 27^{n + 1}}{81^{n}}\)
= \(\frac{3^{n - 1} \times 3^{3(n + 1)}}{3^{4n}}\)
= 3\(^{n - 1 + 3n + 3 - 4n}\)
= 3\(^{4n - 4n - 1 + 3}\)
= 32
= 9
Source: Myschool Past Questions Archive (Record #46096)