how to prime factor using exponents?

Answer 1

First you do the prime factorization, that is find the prime numbers that multiplied with each other make the number you are factoring.
For example look at the number 360. It can be written as 2*2*2*3*3*5
2*2*2 can also be written as 2^3 (Where the 3 is raised a bit, think E=mc^2) This simply means "2 by itself 3 times". Likewise 3*3 can be written 3^2. You could write 5 as 5^1 but usually you don't do that.
So the answer for 360 is: 2^3*3^2*5

Answer 2

Here is an example of what I believe you are asking.

take a number such as 84. It is even so factor by 2
now you have 42. It is even so factor by 2
now you hve 21. 2 + 1 = 3 so factor by 3
now you have 7 which is a prime number and the factoring is complete.

84 = 2 x 2 x 3 x 7 or 84 = 2^2 x 3^1 x 7^1

The same thing for lets say 36.
36 = 2 x 18
18 = 2 x 9
9 = 3 x 3
36 = 2^2 x 3^2