Find the term independent of a in the expansion of `(a^((1)/(3))+(1)/(2a^((1)/(3))))^(18),a gt0`.

Explanation

To find the term independent of \( a \) in the expansion of \( (a^{\frac{1}{3}} + \frac{1}{2a^{\frac{1}{3}}})^{18} \), we will use the Binomial Theorem.

### Step-by-step Solution:

1. **Identify the General Term**:
The general term \( T_{r+1} \) in the binomial expansion of \( (x + y)^n \) is given by:
\[
T_{r+1} = \binom{n}{r} x^{n-r} y^r
...