Find the coefficient of `1/y^10` in the expansion of `(y^3+a^7/y^5)^10`

Explanation

Let (r+1)th term contains `1/y^10`.
` therefore (r+1)`term in the expansion of
`(y^3+a^7/y^5)^10` is `"^10C_r (y^3)^(10-r)(a^7/y^5)^r`
`"^10C_r y^(30-r) a^(7r) y^(-5r) = ^10C_r a^(7r) y^(30-8r)`
`therefore y^(30-8r) = 1/y^10 = y^-10` or , 30-8r = -10 or, 8r = 40 or, r = 5
The coefficient of `1/y^10` is `"^10C_5 a^(7xx5) = (10!)/(5!5!) a^35 = 252a^35`