SOLUTION: I am learning to divide exponents. Can you help me understand why 5 to the 4th power divided by 5 = 5 to the third power BUT 3 divided by 3 to the 3rd power =1/3 to the 2nd power?

Question 661659: I am learning to divide exponents. Can you help me understand why 5 to the 4th power divided by 5 = 5 to the third power BUT 3 divided by 3 to the 3rd power =1/3 to the 2nd power? I cannot find an explanation online or in my book. I am working on a worksheet I printed online that just provides a blank worksheet and then one with the answer. No explanation. I feel like I need a better detailed explanation to understand the different processes for different types of questions. Some have variables like 3r to the 3rd power divided by 2r. The only thing myb book says is to divide the coefficients and subtract the exponents. Thanks!!
Found 2 solutions by Alan3354, josmiceli:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Can you help me understand why 5 to the 4th power divided by 5 = 5 to the third power BUT 3 divided by 3 to the 3rd power =1/3 to the 2nd power?
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BUT 3 divided by 3 to the 3rd power =1/3 to the 2nd power

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
I think it helps to write out the number raised
to a power as a series of multiplications.
Say you have
This is
You can see that when you finish canceling, you have
and this is
This is also
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Now if you turn the fraction upside down,
you've got , and this is

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Try this method. It shows how exponents get added, too

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Hope this helps

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