Showing that $\text{Gal}(\Omega^{X^n -a}_K/K(\zeta_n))$ is Abelian, for char$(K) = 0$ and $0 \not = a \in K$

Question

Let $K$ be a field and $L = \Omega^{X^n -a}_K$ be the splitting field of $X^n-a$. I have already proven that $\zeta_n$ a primitive $n$-th root of unity is in $L$, hence the above question makes sense.