Simplify \(\frac{3^{-5n}}{9^{1-n}} \times 27^{n + 1}\)
A
32
B
33
C
35
D
3
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
\(\frac{3^{-5n}}{9^{1-n}} \times 27^{n + 1}\)
\(\frac{3^{-5n}}{3^{2(1-n)}} \times 3^{3(n + 1)}\)
\(3^{-5n} \div 3^{2(1-n)} \times 3^{3(n + 1)}\)
\(3^{-5n - 2(1-n) + 3(n + 1)}\)
\(3^{-5n - 2 + 2n + 3n + 3}\)
\(3^{-5n + 5n + 3 - 2}\)
\(3^{1}\)
= 3
Source: Myschool Past Questions Archive (Record #27042)