Knowing that we can use Divide-and-Conquer algorithm to compute large exponents, for exemple 2 exp 100 = 2 exp(50) * 2 exp(50), which is quite more efficient, is this method efficient using roots ? For exemple 2 exp (1/100) = (2 exp(1/50)) exp(1/50) ?
In other words, I'm wondering if (n exp(1/x)) is more efficient to (n exp(1/y)) for x < y and where x and y are integers.
There seems to be a method using Dichotomic search and Divide-and-conquer method to know if n exp(1/i) is an Integer. See Dixon's factorisation method : http://en.wikipedia.org/wiki/Dixon's_factorization_method