Mathematics - Binomial Theorem Question with Solution | TestHub

The term $T_{r+1}$ is given by:

$$T_{r+1}={}^{6561}{C}_r{7}^{\frac{6561-r}{3}}11^{r/9}$$

For the term to be free from radical signs, $r$ must be a multiple of 9, and $6561-r$ must be a multiple of 3.

The possible values for $r$ are $0,9,18,27,\dots ,6561$. There are 730 such values.