345
3 x 115
3 x 5 x 23
345 = 3 x 5 x 23
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The prime factorization of 345 is 3 * 5 * 23. Technically, none of these have exponents, but you could argue (and quite correctly) that they are 31 * 51 * 231. Either way, you have 1) no numbers with exponents, or 2) three numbers with exponents, so the answer is false.
No, 3x5x4 is not a prime factorization of 60. A prime factorization of 60 would consist of only prime numbers. The prime factorization of 60 is 2x2x3x5.
When all the factors are prime numbers, that's a prime factorization.
Prime factorization!
There is no need to do prime factorization as prime numbers are already prime.