Q:

If $(x^y)^z = x^{y\cdot z}$, why does $(-5)^{2^{0.5}}$not equal $(-5)^1$? 

As shown by Wolfram Alpha, $(x^2)^{0.5}$ is equal to |x|, but if you tried to simplify it to $x^{2\times {0.5}}$, it would just be $x^1$, or $x$.
Is there some unwritten rule about that distribution law that means you can't do it with fractional exponents? 
Edit: What confuses me the most is how Wolfram Alpha also believes $(x^2)^{0.5}$ = x while actually showing a graph of |x|

A:

With iterated exponentiation the order of the operations are read from the top down.  So in your example one has
$$(-5)^{2^{0.5}}=(-5)^{\left (2^{0.5} \right )}=(-5)^{\sqrt{2}}$$
which is undefined over the reals.  Also note that in general 
$$x^{y^{z}} \neq x^{yz}$$

