a question on spliting field

Question

Let $f$ be a polynomial of positive degree over a field $F$ and $E$ the spliting field of $f$ over $F$ , do there exist
some elements $a_1, a_2, ,…，a_s $ of $F$ and positive integers $n_1,n_2, ,…， n_s$ such that $E=F(a_1^{1/n_1},a_2^{1/n_2},…，a_s^{1/n_s})$ ?

Answer 1

No that is not true. This follows by Abel-Ruffini Theorem (http://en.wikipedia.org/wiki/Abel%E2%80%93Ruffini_theorem).