how to do prime factorization using exponents

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From Yahoo Answers

Question:I have an idea of the answers but I really need some help and just want to make sure they are right.

Answers:13 is a prime number, so just 13 32 = 2^5 198 = 2*11*(3^2)

Question:

Answers:57 = 3 x 19 There is only a single 3 and 19 factor, so you really don't need exponents, but technically it would be to the first power for each: 57 = 3^1 x 19^1

Question:

Answers:2^3x5

Question:42:2x3x7 126:2x3x3x7 Think this is the LCM: 2X3X3X7 72:2X2X2X3X3 108:2X2X3X3X3 Not sure if this is the LCM: 2X2X3X3X3X3 54:2X3X3X3 210:2X3X5X7 hope this is the LCM:3X3X2X5X7 8:2X2X2 30:2X3X5 45:3X3X5 Think that the LCM is correct- LCM: 2X2X3X3X5 Thank You!

Answers:It's better if you write them in exponent form. The general idea is that you take each prime to the highest power in the list and multiply them together. The result if the LCM. 42 = 2 * 3 * 7 126 = 2 * 3^2 * 7 LCM = 2 * 3^2 * 7 72 = 2^3 * 3^2 108 = 2^2 * 3^3 LCM = 2^3 * 3^3 54 = 2 * 3^3 210 = 2 * 3 * 5 * 7 LCM = 2 * 3^3 * 5 * 7 8 = 2^3 30 = 2* 3 * 5 45 = 3^2 * 5 LCM = 2^3 * 3^2 * 5 Hope you can learn from the above examples.

From Youtube

Prime Factorization :This tutorial demonstrates how to find the prime factorization of a number and put it into exponent form. This skill will be used to find Greatest Common Factor and Least Common Multiple later.

factors and primes number 37 :factors and primes number 37 Iknow that my videos may be flawed in some way! I know I rush sometimes and make errors. I know that I'm missing arrows and pointers. I know that you can't see my hand! For egregious errors please tell me and I'll try to get to the corrections. If you can do better, please, do so! Publish! Myself, I'm looking for a teaching job. If you know of a school that can use an English teacher with particular training skills, please let me know. If you agree with Lockhardt www.maa.org then you will find ways to make math more art like and, almost automatically, more agreeable. Unfortunately, with classes of 35:1 or 40:1 teaching is more about crowd control than teaching. And further, I've yet to find any evidence of Lockhardt putting his criticism to work in anything other than idealized situations. Unfortunately, it has proven quite difficult to find much support on the web for math 'doing stuff'. Most of the math exercises found in text books and on the web appear to be not much more than pushing symbols around. If you can suggest ways that math is applied I would very much appreciate your help! If you're studying for a big exam in math or science, nothing brings your study partners into the mix like publishing. Make new smart friends. ;) If you or anyone you knows how to 'do something' especially in math or science... publish that knowledge electronically. Point a web cam at a piece of paper while they solve an abstract problem or use a Livescribe ...