Question 6

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Jambmaths question: 

$\text{Simplify }\frac{{{3}^{-5n}}}{{{9}^{1-n}}}\times {{27}^{n+1}}$

Option A: 

32

Option B: 

33

Option C: 

35

Option D: 

3

Jamb Maths Solution: 

$\begin{align}  & \frac{{{3}^{-5n}}}{{{9}^{1-n}}}\times {{27}^{n+1}}=\frac{{{3}^{-5n}}}{{{3}^{2(1-n)}}}\times {{3}^{3(n+1)}}=\frac{{{3}^{-5n}}\times {{3}^{3n+3}}}{{{3}^{2-2n}}} \\ & \frac{{{3}^{-5n}}}{{{9}^{1-n}}}\times {{27}^{n+1}}=\frac{{{3}^{-5n+3n+3}}}{{{3}^{2-2n}}}=\frac{{{3}^{-2n+3}}}{{{3}^{2-2n}}}={{3}^{-2n+3-(2-2n)}} \\ & \frac{{{3}^{-5n}}}{{{9}^{1-n}}}\times {{27}^{n+1}}={{3}^{-2n+3-2+2n}}=3 \\\end{align}$

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