Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I am trying to prove the following statement:

If $S$ and $T$ are any regular expressions over a 1-letter alphabet and if $n$ is a natural, then the languages $(ST)^n$ and $S^nT^n$ are equal.

share|cite|improve this question

Hint: Show that any two regexps over a $1$-letter alphabet commute, i.e. $PQ = QP$ for every two regexps $P,Q$.

Hint to the hint: Show that any two words over a $1$-letter alphabet commute, i.e. $ab = ba$ for every two words $a,b$.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.