JAMB - Mathematics (2013 - No. 5)
Simplify \(\frac{3^{-5n}}{9^{1-n}} \times 27^{n + 1}\)
32
33
35
3
Explication
\(\frac{3^{-5n}}{9^{1-n}} \times 27^{n + 1}\)
\(\frac{3^{-5n}}{3^{2(1-n)}} \times 3^{3(n + 1)}\)
\(3^{-5n} \div 3^{2(1-n)} \times 3^{3(n + 1)}\)
\(3^{-5n - 2(1-n) + 3(n + 1)}\)
\(3^{-5n - 2 + 2n + 3n + 3}\)
\(3^{-5n + 5n + 3 - 2}\)
\(3^{1}\)
= 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