The exponents are just shorthand for repeated prime numbers. If your prime factorization is 2 x 2 x 2 x 3 x 3 x 3, that's the same as 23 x 33
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The prime factorization of 333 with exponents is 32 x 371
The prime factorization, using exponents, of 160 is: 25 x 5
The prime factorization for 112 using exponents is: 24 x 7
The prime factorization of 999 is 3x3x3x37 or 33x37.
The prime factorization for 53 is: 1 x 53 .Exponents would only get in the way.