48 cubed = 48*48*48
Find factors of 48:
12 and 4
12*4=48
Neither of those numbers are prime factors so we have to break both of then down further.
Find prime factors of 4:
2*2=4
Find factors and prime factors of 12:
12= 4*3
3 is a prime factors but 4 is not. Break down 4 again and get 2*2*3=12
So put that all together and get the prime factors of 48, they are:
2*2*2*2*3
The prime factor of 48 cubed is the same thing as the prime factor of 48 three times
The prime factors are:
2*2*2*2*2*2*2*2*2*2*2*2*3*3*3
(12 2's and 3 3's)