Find the number of reational is exponets of `(9^(1//4)+8^(1//6))^(1000)`

Explanation

The general term in the expansion of `(9^(1//4)+8^(1//6))^(1000)` is
`T_(r+1)=""1000C_(r)(9^(1/4))^(1000-r)=(8^(1/6))^r=""^1000 C_(r) 3^((1000-r)/(2)) 2 ^(r/2)`
The above term will be rational if exponents of 3 and 2 are integers
It means `(1000-r)/(2) " and " r/2 ` must be integers
The possible set of values of r is { 0,2,4 ..... 1000}
Hence s, number of rational terms is 501