A regular expression $r$ is said to be in disjunctive normal form if it can be written in the form $r = r_1 +r_2 +\dots+r_n$ for some $n ≥ 1$, where none of the regular expressions $r_1, r_2, \dots, r_n$ contains the symbol $+$ (union).
For example, the regular expression $a^*b^* + (ab)^* + (c(acb)^*)^*$ is in disjunctive normal form.
The task is to prove that every regular language can be specified by a regular expression in disjunctive normal form. Considering that every regular language by default can be represented by a regular expression, the question now seems to simplify to proving that any regular expression can be converted to or expressed in disjunctive normal form. Any idea on how that is possible?