Properties power functions

Introduction: A function of the form $y(x)=x^{\frac{m}{n}}$, with $m$ and $n$ integer ($n \neq 0$), is called a power function.

Theorem: Power functions have the following properties:

1. $x^p \cdot x^q=x^{p+q}$
2. $\frac{x^p}{x^q}=x^{p-q}$
3. $(x^p)^q=x^{pq}$
4. $x^p \cdot y^p =(x\cdot y)^p$
5. $x^0 = 1$