Rationals except Zero

Here’s a quick one: All rational numbers except 0 can be expressed as $$(-1)^s \Pi p_i^{n_i}$$ where $s \in \{0, 1\}$, $p_i$ is a prime number, and $n_i$ is an integer.

This reminds me of the restriction on the definition of rationals, i.e., that $\frac{a}{b}$ is a rational number for all integers $a$ and $b$ except $b = 0$. However, this can be written to make zero less exceptional: All rational numbers can be written in the form $\frac{a}{b}$ where $a \in \mathbb{Z}$ and $b \in \mathbb{N}^*$.