Problem calculating an expression with roots

[Snorre]

Hello Reto,

In Home it seems to be related to evaluation order: 1/3 is evaluated to the approximated floating 0.333 first. There seems to be no further internal test if the exponent is rational.
If you enter it as ³√(-8) you'll get -2.
(The other way around is similiar: (1/3)NTHROOT(-2) is not the same as (-2)^3)

The CAS seems to evaluate (-1)^(p/q) to the first complex solution as long as the denominator q is ≤4 (autosimplification turned off).
Sorry, can't tell you why (just guess).