Wrong basic exponential rule: $(a^b)^c\neq a^{bc}$ I've been searching about exponential rules on google and the first three results was these ones: 
Link 1
Link 2
Link 3
I didn't understand why they all say: $(a^b)^c=a^{bc}$. This is wrong, see for example: $((-2)^{2})^{1/2}=2\neq (-2)^1$.
Why does every site I read say this wrong rule? how can I reformulate this to make it true?


Why does every site I read say this wrong rule?

All these sites you found appear to be aimed at a beginning algebra audience.  At this level, typically all bases are positive and all exponents are integers (at least to begin with).  And with positive bases and integer exponents, it is indeed the case that $(a^m)^n = a^{mn}$.  At this level, in the US at least, one should never expect to see something like $(-2)^{1/2}$ because that ventures into the realm of imaginary numbers, which is not typically covered until 2-3 semesters after beginning algebra.

how can I reformulate this to make it true?

All you really need is $a > 0$, then for any $m, n \in \Bbb R$, we have $(a^m)^n = a^{mn}$.  If $a = 0$ then you have to worry about negative exponents because they'll lead to division by zero.  If $a < 0$ then it is not true in general that $(a^m)^n = a^{mn}$, as you've already noted with your example.
