The sum of all rational terms in the expansion of `(3^(1/5) + 2^(1/3))^15` is

Explanation

The general term in the expansion of `(3^(1//5) + 2^(1//3))^(15) ` is
` T_(r + 3) = ""^(15)C_(r) (3^(1//5))^(15-r) .(2^(1//3))^(r)`
` = ""^(15)C_(r) - 3^(-(r)/(5) . (r)/(2^(3)))`
Now `0 le r le 15 `
From r = 0 , 15
Then ` T_(0 + 1) = ""^(15)C_(0) * 3^(3) * 2^(5) = 27`
and ` T_(15 + 1) = ""^(15)C_(15) * 3^(3) . 2^(5) = 32 `
` therefore ` Sum of all rational terms 27 + 32 = 59 .