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Verified Answer :

48 cubed = 484848

Find factors of 48:
12 and 4
124=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= 43
3 is a prime factors but 4 is not. Break down 4 again and get 2
23=12

So put that all together and get the prime factors of 48, they are:
2
2223

The prime factor of 48 cubed is the same thing as the prime factor of 48 three times

The prime factors are:
2
2222222222233*3
(12 2's and 3 3's)