How is $x^a$ for $x \in \mathbb{R},a>0$ defined?
For $x>0$ I think one can define it as $e^{a ln(x)}$. For $x<0$ I am not sure anymore. I think that $x^\frac{3}{5}=(x^5)^\frac{1}{3}$ makes sense somehow but for $x^\frac{3}{2}$this doesn't work anymore. Maybe somebody knows how to define these power functions properly.