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I am trying to prove something and I am on the right track (I think). But I need help on how to accurately describe what I want to do mathematically. Further explanation in the comments.

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Hi u/softclick,

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First of all, this is only a draft I will make it prettier and add explonations to the steps later!
  
So my Idea was something like this:
  

  
5\^5 >= 2\^2 \* 3\^3
  
= 5\*5\*5\*5\*5 >= 2\*2\*3\*3\*3
  

  
so we have 5 factors on both sides and since 2+3 = 5 each of them have to be less or equal to 5.
  
therefore the right side must be less or equal to 5\^5.
  

  
But I dont know how to write down the "we have n factors on both sides" step in proper math
  
(also: no clue what flair to use, im sorry)

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