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The 5th power of a positive number is equal to the product of 1/3 and the 6th power of the number. What is the ratio of this number's 12th power to its 9th power? Express your answer as a common fraction.

 Oct 25, 2022
 #1
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The ratio is 3/5.

 Oct 25, 2022
 #2
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The 5th power of a positive number is equal to the product of 1/3 and the 6th power of the number. What is the ratio of this number's 12th power to its 9th power? Express your answer as a common fraction.  

 

  x5        x6  

–––  =  –––      Dividing both sides by x5,    x = 3  

  1         3  

 

 

  x12          x3  

––––   =  ––––  =   33  =  27  

   x9           1  

 Oct 25, 2022

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