instead of 1/3 (since otherwise it would raise it to the first and then divide by three)
Either you're not using parentheses correctly, or your calculator is badly broken. Parenthetical expressions are evaluated first and the calculation should reduce to -270.333..
It is a problem of the Windows Vista Calculator then. In Windows 7 it works perfectly.
Just out of curiosity, try: (-27)^(1/3) in the calculator to see if you get an answer.
That won't work. If you compute 1/3 as a floating-point number it will be rounded to some fraction with a power of 2 in the denominator, and now -27 raised to that power won't be a real number.
In C99 and C++11 you have the function `cbrt', which will give you the correct value, but if you use `pow', you'll get `nan'.
That won't work
Actually it does in Windows 7's calculator. Windows calculator uses arbitrary precision numbers or it just performs symbolic optimization.
Regardless, I hadn't thought about floating point issues when doing the cubic root of a number in C++,so I am glad you pointed out that converting roots to powers is not a good idea when it comes to negative numbers, as a rule 
