Problem calculating an expression with roots

[retoa]

(02-02-2015 12:53 PM)parisse Wrote:  ...because the expression is not defined for all values of x (or ambiguous like the definition of x^(1/3) for x<0).

Parisse, I agree with you that working with nth roots is not very useful, I think I never found such expressions in real life calculation and it is very difficult to find practical examples with roots above the 3rd (except the 12th root of 2 in music, but you don't have a variable in it).

But I still have a question about x^(1/3) for x<0.

If I try to calculate (-8)^(1/3), one solution is -2, because (-2)^3=-8

In CAS mode the Prime gives one of the complex solutions, 1+sqrt(3) i
In home it gives the complex solution if you enable complex numbers and an error if you don't.
3rd root of (-8) gives -2 (both in home and CAS)

Why does the Prime give a complex solution to (-8)^(1/3) and not the trivial one -2?
And why does the Prime in home mode not give the -2 solution when it works with real numbers?

As a comparison I tried to calculate (-8)^(1/3) on other platforms:

HP 11C : Error 0
HP 35s : INVALID y^x (or 1 i sqrt(3) if you use -8 i 0 )
Casio fx82 solar : -2
TI-30X Pro : -2
TI nspire CAS : -2
WP 34S : Domain Error
Elektronika MK56 : Error
Calculator application in linux mint: -2
Maxima : -2
Wolfram aplha : 1+sqrt(3)i

So it seems to be more a philosophical question, cause any producer choose his own way, but would it not be better to give the real solution -2 ?

Kind regards

Reto