Roots vs fractioned powers?

[WhiteBlackGoose]

That is quite a vague and ambiguous topic when it comes to computational algebra. As we know, n-th root is something whose n-th power is the root's argument. So technically there are a lot of such numbers. The simplest way to represent a root is fractioned powers, e. g. square root of x is x^(1/2).

There we come to another problem: we know that (x ^ a) ^ b = x ^ (a * b), and we know, that 1/2 * 2 = 1. So technically we get that sqrt(x^2) = x which is actually okay to me, but in most common cases it won't be accepted. Reason: principle root.

There're more ambiguous stuff, I might add some more info to this issue. Any thoughts are welcomed and may be discussed in this thread.