Question

If $3^9.3^{12}.3^{15}.3^n$ is a perfect cube (of an integer ) where $n\in N$, then find the value of n.

• A. $18$
• B. $14$
• C. $16$
• D. $17$

Answer 1

The correct option is A $18$

Given

$3^9{.3}^{12}{.3}^{15}{.3}^n$

$⟹3^{9+12+15+n}$

$⟹3^{36+n}$

For the term to be perfect cube

$36+n$ should be multiple of $3$

From the given options

$18$ is only the option that can turn the given expression as cubic number

$⟹n=18$