Simplify 3 n 1 27 frac n 1 81 n - JAMB Mathematics 2017 Question
Simplify 3 \(^{n − 1}\) × 27 \(\frac{n + 1}{81^n}\)
A
3\(^{2n}\)
B
9
C
3n
D
3 \(^{n + 1}\)
correct option: b
3\(^{n + 1}\) × 27\(\frac{n + 1}{81^n}\)
= 3\(^{n + 1}\) × 3 \(\frac{3^{(n + 1)}}{3^{4n}}\)
= 3\(^{n + 1 + 3n + 3 − 4n}\)
= 3\(^{4n − 4n − 1 + 3}\)
= 32
= 9
= 3\(^{n + 1}\) × 3 \(\frac{3^{(n + 1)}}{3^{4n}}\)
= 3\(^{n + 1 + 3n + 3 − 4n}\)
= 3\(^{4n − 4n − 1 + 3}\)
= 32
= 9
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