Simplify 3 \(^{n − 1}\) × \(\frac{27^{n + 1}}{81^n}\)
- 3\(^{2n}\)
-
9
- 3n
- 3 \(^{n + 1}\)
The correct answer is: B
Explanation
3\(^{n - 1}\) × \(\frac{27^{n + 1}}{81^n}\)
= 3\(^{n - 1}\) × \(\frac{3^{3(n + 1)}}{3^{4n}}\)
= 3\(^{n - 1 + 3n + 3 − 4n}\)
= 3\(^{4n − 4n − 1 + 3}\)
= \(3^{2}\)
= 9
There is an explanation video available .