Power of Positive Real Number is Positive/Rational Number

Theorem
Let $x \in \R_{>0}$ be a (strictly) positive real number.

Let $q \in \Q$ be a rational number.

Then:
 * $x^q > 0$

where $x^q$ denotes the $x$ to the power of $q$.

Proof
Let $q = \dfrac r s$, where $r \in \Z$, $s \in \Z \setminus \set 0$.

Then:

Hence the result.