2) = (x^m)*(x^m)*…(x^m) 2) Definition of exponent

(n times)

3) = (x * x * x *…*x) * (x * x * x *…*x) * … * (x * x * x *…*x) 3) As above

(m times)

4) = x * x * x *… *x 4) Associative Property of Multiplication

5) = x^(mn) 5) Definition of multiplication

First – given the way Yahoo messes with formatting, I hope you can read it. Second – I left out a step between 4 and 5 because I felt it unnecessary. If you understand the proof, you should be able to see what step I left out. Third – there are other possible reasons for step 5. I picked the one I felt fit best, but you might want to look for others, too.