Find the number of terms which are free from radical signs in the expansion of `(y^(1//5)+x^(1//10))^(55)dot`

The number of terms free from radical sign in the expansion of (1+3^((1)/(3))+7^((1)/(7)))^(10) is

The number of irrational terms in the expansion of (2^(1//5) + 3^(1//10))^(55) is

If the number of terms free from radicals in the expansion of (7^((1)/(3))+11^((1)/(9)))^(6561) is k, then the value of (k)/(100) is equal to

The number of irrational terms in the expansion of (4^((1)/(5))+7(1)/(10))^(45) is

The number of rational terms in the expansion (2^((1)/(5))+3(1)/(10))^(45) is

Find the number of irrational terms in the expansion of (5^(1/6)+2^(1/8))^(100)