I'm having some trouble understanding the regular expression $0^*10|01(01)^*$. The expression matches strings like $00010$. But for some reason, I wasn't able to find a string that matches the $(01)^*$ at the end. An equivalent expression with capturing groups to demonstrate the order of evaluation would be very much helpful.
For a regular expression $r$, the regular expression $r^*$ matches all words of the form $w_1 \ldots w_n$, where $w_1,\ldots,w_n$ are matched by $r$ (possibly $n = 0$). For example $01$ matches only the word $01$, and so $(01)^*$ matches the words $\epsilon, 01, 0101, 010101, \dots$