Question : The value of $\frac{(243)^\frac{n}{5}\times 3^{2n+1}}{9^{n}\times 3^{n-1}}$ is:
Option 1: 3
Option 2: 9
Option 3: 6
Option 4: 12
Answer (1)
23rd Jan, 2024
Correct Answer: 9
Solution :
Given: $\frac{(243)^\frac{n}{5}\times 3^{2n+1}}{9^{n}\times 3^{n-1}}$
= $\frac{(3^5)^\frac{n}{5}\times 3^{2n+1}}{3^{2n}\times 3^{n-1}}$
= $\frac{3^n\times 3^{2n+1}}{3^{2n}\times 3^{n-1}}$
= $\frac{3^{3n+1}}{3^{3n-1}}$
= $\frac{3^{3n}×3^1}{3^{3n}×3^{-1}}$
= ${3^{2}}$
= $9$
Hence, the correct answer is 9.
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