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

Explanation

In the expansion of `((x)/(3)+9y)^(1)`
`:.` No. of terms =10 +1 =11 (dd)
`:.` Middle term `-(11+1)/(2)`th terms
=6th term
`:.` Middle term `=T_(6)=T_(5+1)`
`=^(10)C_(5).((x)/(3))^(10-5).(9y)^(5)`
`=(|ul10)/(|ul5.|ul5)xx(x^(5))/(3^(5)).(3^(2))^(5)y^(5)`
`=(10xx9xx8xx7xx6)/(5xx4xx3xx2xx1)xx3^(5)x^(5)y^(5)`
`=61236 x^(5)y^(5)`