Power Function on Base between Zero and One Tends to One as Power Tends to Zero/Rational Number

Theorem
Let $a \in \R_{> 0}$.

Let $0 < a < 1$.

Let $f: \Q \to \R$ be the real-valued function defined as:
 * $f \left({q}\right) = a^q$

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

Then:
 * $\displaystyle \lim_{x \mathop \to 0} f \left({x}\right) = 1$