If $$\root 3 \of {{3^n}} {\text{ = 27,}}$$   then the value of n is = ?

A. 9

B. 6

C. 1

D. 3

Answer: Option A

Solution(By Examveda Team)

According to question,
$$\eqalign{ & \root 3 \of {{3^n}} {\text{ = 27}} \cr & \Rightarrow {\left( {{3^n}} \right)^{\frac{1}{3}}} = {\left( 3 \right)^3} \cr & \Rightarrow {3^{\frac{n}{3}}} = {3^3} \cr & \Rightarrow \frac{n}{3} = 3 \cr & \Rightarrow n = 9 \cr} $$