What's $(-1)^{2/3}\; $? I know that 
$\left ( -1 \right )^{2/3}=\left ( \left ( -1 \right )^{2} \right )^{1/3}=1$
But Matlab computes this as $- 0.5 + 0.8660254038i$ a complex number.Why?

Terminology. The way Matlab seems to be seeing this, when you ask for $k^{2/3}$, you are asking for the number $z$ that solves the equation
$$
z^3 = k^2.
$$
In case $k = -1$, there are three solutions to this equation in the complex plane, one of which happens to be the real number 1, and for some reason Matlab has instead given you the one in the second quadrant. I am a little surprised that it is reading the input this way; it seems to me that from the standpoint of applied math it ought to return the unique real root when it exists, unless you specifically ask it not to.
