p-adic norm, Sets equal Let $p$ a prime, and the p-adic norm $|x|_p = (\frac{1}{p})^{v_p(x)}$, with $v_p$ the p-adic valuation. Show that 
$$\{ |x|_p : x \in \mathbb{Q}_p \}  = \{ p^k : k \in \mathbb{Z}\}$$
My question is how to show $\supseteq$? $\subseteq$ is easy!
Thanks!

Hint: think about powers of $p$! $\mathbb{Q}\subseteq\mathbb{Q}_p$, and you should know that $|\mathbb{Q}|_p$ is your desired set.
