Take the following:
$$f(x) = x^{6/4}$$
The domain of this function is all real numbers. This function can be simplified to:
$$f(x) = x^{3/2}$$
The domain of this function is all real numbers greater than or equal to 0. Why is this true? Why does simplifying the function change its domain?
The problem is that $$ x^{(m/n)} = (x^m)^{1/n} $$ is only valid if $x$ is positive. So in other words, while of course it is true that $x^{(6/4)} = x^{(3/2)}$, you seem to be interpreting this to mean $(x^6)^{1/4} = (x^3)^{1/2}$, which doesn't follow.