Find the middle terms in the expansions of `(x/3+9y)^10`

Explanation

To find the middle term in the expansion of \((\frac{x}{3} + 9y)^{10}\), we can follow these steps:

### Step 1: Identify \(n\) and determine the middle term
The given expression is \((\frac{x}{3} + 9y)^{10}\). Here, \(n = 10\). Since \(n\) is even, the middle term can be found using the formula for the \( \frac{n}{2} + 1 \) term.

**Calculation:**
\[
\text{Middle term} = T_{\frac{n}{2} + 1} = T_{5 + 1} = T_6
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