SOLUTION: 5^5/5^4=

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Question 603719: 5^5/5^4=
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
By definition,
5%5E5%2F5%5E4=+5%2A5%2A5%2A5%2A5%2F%285%2A5%2A5%2A5%29
and you know in multiplication of fractions and integers that
, so


In the same way, whenever you are dividing powers of the same base number, you end up with exponents that are differences of the exponents
5%5E6%2F5%5E4=5%5E%28%286-4%29%29=5%5E2 and the 5%5E5%2F5%5E4=5 that we found can be written as 5=5%5E1=5%5E%28%285-4%29%29
5%5E3%2F5%5E7=1%2F5%5E%28%287-3%29%29=1%2F5%5E4 sometimes expressed as 5%5E-4

IMPORTANT NOTE:
When you cannot write a long horizontal fraction line, you have to write some parentheses.
The horizontal fraction bar includes invisible brackets enclosing the expressions above and below, so
5%2A5%2A5%2A5%2A5%2F%285%2A5%2A5%2A5%29 = (5*5*5*5*5)/(5*5*5*5)
In this case, you could skip the first set of brackets because
5*5*5*5*5/(5*5*5*5)= (5*5*5*5*5)/(5*5*5*5)=5%2A5%2A5%2A5%2A5%2F%285%2A5%2A5%2A5%29
However, according to rules of order of operation, doing multiplications and divisions from left to right,
5*5*5*5*5/5*5*5*5 means %285%2A5%2A5%2A5%2A5%2F5%29%2A5%2A5%2A5=5%2A5%2A5%2A5%2A5%2F5%2A5%2A5%2A5