On an algebraic calculator like the TI-89 or the Casio Classpad, you can type in (-8)^(1/3). In "complex" mode you get the complex root, and in "real" mode you get the real one. In this case the calculator can "see" the entire equation, and notice the special case of a rational power with an odd denominator.

On an RPN calculator without an Nth root function, the software has no opportunity to notice you are raising to a rational power with an odd denominator. It just sees you raising -8 to the power of .33333333 (the *truncated* result of taking the reciprocal of 3) -- which is *NOT* the same thing as 1/3.

Now it could do some wacky stuff like try and recognize the truncated real decimal representation as a rational number, but that sort of magic is why my Casio fx-5800p thinks 80143857/25510582 is Pi. I think I would rather not have the magic.

What you can do is code up an Nth root program that notices the special cases, and tries to deliver a real number when it can.