Roots vs fractioned powers?

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.