Home » Past Questions » Mathematics » Simplify \(\frac{3^{-5n}}{9^{1-n}} \times 27^{n + 1}\)

Simplify \(\frac{3^{-5n}}{9^{1-n}} \times 27^{n + 1}\)


Question

Simplify \(\frac{3^{-5n}}{9^{1-n}} \times 27^{n + 1}\)

Options

A) 32

B) 33

C) 35

D) 3

The correct answer is D.

Explanation:

\(\frac{3^{-5n}}{9^{1-n}} \times 27^{n + 1}\)
\(\frac{3^{-5n}}{3^{2(1-n)}} \times 3^{3(n + 1)}\)
\(3^{-5n} \div 3^{2(1-n)} \times 3^{3(n + 1)}\)

\(3^{-5n - 2(1-n) + 3(n + 1)}\)

\(3^{-5n - 2 + 2n + 3n + 3}\)
\(3^{-5n + 5n + 3 - 2}\)
\(3^{1}\)
= 3


More Past Questions:


Dicussion (1)

  • \(\frac{3^{-5n}}{9^{1-n}} \times 27^{n + 1}\)
    \(\frac{3^{-5n}}{3^{2(1-n)}} \times 3^{3(n + 1)}\)
    \(3^{-5n} \div 3^{2(1-n)} \times 3^{3(n + 1)}\)

    \(3^{-5n - 2(1-n) + 3(n + 1)}\)

    \(3^{-5n - 2 + 2n + 3n + 3}\)
    \(3^{-5n + 5n + 3 - 2}\)
    \(3^{1}\)
    = 3

    Reply
    Like