According to index laws, $(a^b)^c=a^{b\cdot c}=(a^c)^b$
However, if for example we have $a=-1, b=4, c=1/2$, then we get the equation:
$$((-1)^4)^{1/2}=(-1)^2=((-1)^{1/2})^4$$
The first equation is equal to $1$, however, the last one is undefined. How is this possible?
P.S. I'm sorry the formatting of the indexes is not ideal, I'm not sure how to do it properly
Attention the exponent law you give is only true under certain assumptions. A few example:
If $a \in \mathbb R$ and $b,c \in \mathbb Z$ then $a^{bc} = (a^b)^c$
If $a \in \mathbb R$, $a > 0$ and $b,c \in \mathbb{R}$ then $a^{bc} = (a^b)^c$
But $a^{bc} = (a^b)^c$ is not always true for $a,b,c \in \mathbb{R}$... In particular if $a<0$ and $b$ or $c$ is not an integer.