Way 1:  Factor Trees

Let's just do one!

Find the prime factorization of 84:

First, see if you can think of times tables numbers:

84  ...  splits into 12 and 7  ...  We're splitting the number with branches like a tree!

 

84  ...  splits into 12 and 7  ...  12 isn't prime, so we keep going  ...  7 is prime, so circle him!  That branch stops.

 

84  ...  splits into 12 and 7  ...  12 splits into 4 and 3  ...  3 is prime!  Circle him and stop that branch  ...  4 isn't prime, so keep going...

 

84 splits into 12 and 7  ...  12 splits into 4 and 3  ...  splits into 2 and 2  ...  Both primes!  Done!

 

Now you just write it out:

84 = 2 x 2 x 3 x 7
 

Here it is in exponents:

84 = 2^2 x 3 x 7