In `( 2^(1/3)+1/3^(1/ 3))^n` if the ratio of 7th term from the beginning to the 7th term from the end is 1/6, then find the value of `ndot`

Options

A. `6`
B. `9`
C. `12`
D. `15`

Explanation

To solve the problem, we need to find the value of \( n \) given that the ratio of the 7th term from the beginning to the 7th term from the end in the expansion of \( (2^{1/3} + 3^{-1/3})^n \) is \( \frac{1}{6} \).

### Step-by-step Solution:

1. **Identify the 7th term from the beginning (T7)**:
The \( k \)-th term in the binomial expansion is given by:
\[
T_k = \binom{n}{k-1} (a)^{n-k+1} (b)^{k-1}
...