Ok so let me explain my self. We all know that the $\sqrt{X}$ is defined only for $X\ge 0$ (not considering complex numbers). But what if I write $X^{2/4}$ which is the 4th root of $X^2$, and now it's defined on any $X$? (The $\mbox{2n}$th root is defined only for non negative numbers and $X^2$ is non negative obviously so the $\mbox{2n}$th root is defined for this example $n=2$).
So long story short:
$X^{1/2}$ defined for non negative $X$.
$X^{2/4}$ defined for All $X$.
$1/2 = 2/4.$
What am I missing here?
$1/2$ is the same as $2/4$, so $X^{1/2}$ is the same as $X^{2/4}$. However, this is not necessarily the same as $(X^2)^{1/4}$. The "laws of exponents" must be modified when dealing bases that are not positive reals.