Let's take 140 as an example. To find its prime factors we firstly divide it by 2 until it won't divide any further, then by 3, then by 5, then by 7, ... . We find that 2 divides twice with 35 as quotient, then 5 once with 7 as quotient, then 7 once with 1 as quotient; so stop. We have 140 = 2 x 2 x 5 x 7. The exponential notation says that if a number p occurs more than once in a repeated product, say t times, instead of writing p x p x ... x p (t times), you write p^t, which is keyboard for p with t written superscript (above and to the right). So 140 = 2^2 x 5 x 7. You could write 5^1 and 7^1 here, since 5 occurs 1 time and 7 occurs 1 time, but that would not save any ink. Simpler examples: 12 = 2^2 x 3; 100 = 2^2 x 5^2; 432 = 2^4 x 3^3.