Question on: JAMB Mathematics - 2013
Simplify \(\frac{3^{-5n}}{9^{1-n}} \times 27^{n + 1}\)
A
32
B
33
C
35
D
3
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Correct Option: D
\(\frac{3^{-5n}}{9^{1-n}} \times 27^{n + 1}\)
\(\frac{3^{-5n}}{3^{2(1-n)}} \times 3^{3(n + 1)}\)
\(3^{-5n} \div 3^{2(1-n)} \times 3^{3(n + 1)}\)
\(3^{-5n - 2(1-n) + 3(n + 1)}\)
\(3^{-5n - 2 + 2n + 3n + 3}\)
\(3^{-5n + 5n + 3 - 2}\)
\(3^{1}\)
= 3
\(\frac{3^{-5n}}{3^{2(1-n)}} \times 3^{3(n + 1)}\)
\(3^{-5n} \div 3^{2(1-n)} \times 3^{3(n + 1)}\)
\(3^{-5n - 2(1-n) + 3(n + 1)}\)
\(3^{-5n - 2 + 2n + 3n + 3}\)
\(3^{-5n + 5n + 3 - 2}\)
\(3^{1}\)
= 3
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