SOLUTION: evaluate 5^2 over 5^5

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Question 183050This question is from textbook Algebra 2
: evaluate 5^2 over 5^5 This question is from textbook Algebra 2

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Here's the long way to do it:


%285%5E2%29%2F%285%5E5%29 Start with the given expression.


%285%2A5%29%2F%285%5E5%29 Expand 5%5E2 to get 5%5E2=5%2A5


%285%2A5%29%2F%285%2A5%2A5%2A5%2A5%29 Expand 5%5E5 to get 5%5E5=5%2A5%2A5%2A5%2A5 (note: there are five 5's)


Highlight the common terms.


%28cross%285%29%2Across%285%29%29%2F%28cross%285%29%2Across%285%29%2A5%2A5%2A5%29 Cancel out the common terms.


1%2F%285%2A5%2A5%29 Simplify


1%2F125 Multiply 5%2A5%2A5 to get 5%2A5%2A5=5%2A%285%2A5%29=5%2A25=125



So %285%5E2%29%2F%285%5E5%29=1%2F125


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Here's the short way to do it:


%285%5E2%29%2F%285%5E5%29 Start with the given expression.


5%5E%282-5%29 Divide the terms by subtracting the exponents.


5%5E%28-3%29 Subtract


1%2F%285%5E3%29 Flip the base to make the exponent positive.


1%2F%285%2A5%2A5%29 Expand 5%5E3 to get 5%5E3=5%2A5%2A5


1%2F125 Multiply 5%2A5%2A5 to get 5%2A5%2A5=5%2A%285%2A5%29=5%2A25=125



So %285%5E2%29%2F%285%5E5%29=1%2F125