JAMB 2017 · UTME (set 2) · Q11

Simplify $\dfrac{3^{n-1} \times 27^{n+1}}{81^n}$ .

Worked solution (try it first)

Write everything as a power of 3: $27^{n+1} = 3^{3n + 3}$ and $81^n = 3^{4n}$ .
Top: add the indices, $(n - 1) + (3n + 3) = 4n + 2$ , so the top is $3^{4n + 2}$ .
Divide: subtract the indices, $(4n + 2) - 4n = 2$ .
So the value is $3^2 = 9$ , option B.