what will be kleene star "expansion" of expression $a^*b^*$ in lexicographic order? I'm confused and I really want to clear my concepts so I can proceed further
The lexicographic order is defined on words, not on regular expressions. An interesting exercise is to describe the restriction of the lexicographic order to the language $a^*b^*$, assuming that $a < b$. Note for instance that $1 < a < a^2 < \dotsm < a^n < \dotsm$, but $\dotsm <a^nb <\dotsm <a^2b < ab < b$.