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I would like to know if this is a valid application of the Enumeration Principle. Thanks in advance.

Claim: For any natural number $n$, $\mathbb{Q}^n$ is countable.

Proof. Let $n\in\mathbb{N}$. Consider the set $\mathcal{L} = \left\{ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, -, /, * \right\}$. For any $x = (x_1, \ldots, x_n)\in\mathbb{Q}^n$, each $x_i$ can be labelled by elements of $\mathcal{L}$ and therefore each $x$ can be labelled by elements of $\mathcal{L}$. For example, we can label $(\frac{1}{2}, -30, 4)$ by the sequence $(1, /, 2, *, -, 3, 0, *, 4)$, where the asterisk is used to separate components. Hence, $\mathbb{Q}^n$ can be labelled by a countable set. By the Enumeration Principle, $\mathbb{Q}^n$ is countable.

For anyone who's interested: