I am having trouble understanding this topic in algebra. Can you guys please help?

My question is what is the splitting field for x^3-2 over Q. In my book there is an example that says for x^n-a over Q a^1/n, wa^1/n, ..., w^n-1 * a^1/n are zeroes of x^n-a in Q(a^1/n, w) (w is primitive nth root of unity)

So does that mean that the splitting field for my problem would be: Q(2^1/3, w)? why?