Products and Powers of Countable Sets

Let $X$ and $Y$ be sets and let $\mathbb{N}$ be the set of natural numbers. Then the following hold.

1. (Products.) If $X$ and $Y$ are countable, then the Cartesian product $X\times Y$ is countable.

2. (Powers.) If $X$ is countable and $k\in\mathbb{N}$, then the set $X^{k}$ of $k$-tuples in $X$ is countable.