Construct a DFA for the following language: L={a^n b^n | n>=1}

Question

in the language, n is power but I didn't know how to write.

Answer 1

I think you misunderstood your homework (not to mention the classes themselves). That language isn't regular. What that means is, you can't construct a DFA for it.

Think about it: as you're going through the loop over a, you're not holding anywhere the number of times you executed the state. You have no way of knowing how many times to read b.

This can be done with a context free grammar like this however:

S->aSb|ab

Answer 2

Did you go over the Regular Pumping lemma in your class?

There's a similar pumping lemma for Context Free languages as well