Why do we need a positive base for a fractional exponent

Question

In my school book it says that if $f(x) =$ $x^{\frac{m}{n}}$. The base ($x$) should be greater than $0$ or in other words $Af=(0,+\infty)$. Why is that? If the base is negative I run to the contradiction that while $(-1)^3 = -1$, if you write it as $(-1)^{\frac{6}{2}}$ then it is the square root of $x^6 $which is equal to $1$ and not $-1$. Why does this happen and what constraints do I have to get to use fractional exponents on negative numbers? Thanks