This page describes an algorithm: http://mathforum.org/library/drmath/view/55896.html. x^(1/n) = the nth root of x, and x^mn = (x^m)^n. Thus, x^(m/n) = (the nth root of x)^m. Arbitrary roots can be calculated with Newton's method. Integer powers can be calculated with Exponentiation by squaring. For irrational exponents, you can use increasingly accurate rational approximations until you get the desired number of significant digits.
Is this what you already tried? Why is it causing overflow?