Isomorphism Galois group

Question

I would like to show that if we take $\mathbb{Q}_p \subset K \subset \overline{K}$ where $K$ is a finite extension and $\overline{K}$ an algebraic closure of $K$ then we have $$Gal(\overline{K} /K)^{ab} \simeq \widehat{(K^{\times})} $$ Where $\widehat{(K^{\times})}$ is the profinite completion of $K^{\times}$. Any ideas ?