SOLUTION: I am working on 'notations', and understand how to work out things like '5 to the power of 4'...but now I need to work in reverse and I can't work out how to do that without just u

Question 541791: I am working on 'notations', and understand how to work out things like '5 to the power of 4'...but now I need to work in reverse and I can't work out how to do that without just using trial and error! The first question I was lucky, as I'd already worked out '5 to the power of 4' as an earlier question so knew when asked to 'simlify 625' that it was 5 to the power of 4 (large 5 then little 4 - can't figure out how to type that on the computer!). The next question is 'simplify 729'....there are another 8 similar questions...I can't just run through each number trying to times it by itself until it hits the right answer or goes over so then move onto the next number!
My question is, what is the mathmatical/scientific/proper way to do this! If you need a specific question, simplify 729 is fine, but I need how to work it out more than I need the actual answer to that question!
I'm sorry if I've gone to the wrong section. Thank-you for your time and patience.
Lily
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
suppose you take the number
2187
factorize the number by prime factors (2,3,5,7,11,13,17,etc
keep on dividing . 2187/3 = 729. 729/3=243
3 | 2187
3| 729
3{243
3|81
3|9
3|3
3|1
you have 3*3*3*3*3*3 = 3^6
Same can be applied to any number
m.ananth@hotmail.ca
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