Prime factorization is dividing a number by prime numbers (starting with 2) until you reach a final, last number (has to be a prime number. So 670 = 2 x 5 x 67. In this case there is no repetition of any number, thus there is no need for exponents.

No. Every composite number has one unique prime factorization. You can write it with or without exponents, but it's still the same prime factorization.

Dividing fractions invole multiplacation because you can use it too see how many time's a number goes into another answer. And that is why dividing involves multiplacation.

That appears to be the prime factorization of 14175. If you compare that to the prime factorization of another number, you will be able to find the LCM between the two.