Simplify 3 \(^{n − 1}\) \times \(\frac{27^{n + 1}}{81^n}\)
A
3\(^{2n}\)
B
9
C
3n
D
3 \(^{n + 1}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
3\(^{n - 1}\) \times \(\frac{27^{n + 1}}{81^n}\)
= 3\(^{n - 1}\) \times \(\frac{3^{3(n + 1)}}{3^{4n}}\)
= 3\(^{n - 1 + 3n + 3 − 4n}\)
= 3\(^{4n − 4n − 1 + 3}\)
= \(3^{2}\)
= 9
Source: Myschool Past Questions Archive (Record #46331)