Question 603719
By definition,
{{{5^5/5^4= 5*5*5*5*5/(5*5*5*5)}}}
and you know in multiplication of fractions and integers that
{{{5*5*5*5*5/(5*5*5*5) =(5/5)*(5/5)*(5/5)*(5/5)*5 }}} , so
{{{5^5/5^4= 5*5*5*5*5/(5*5*5*5)=(5/5)*(5/5)*(5/5)*(5/5)*5=1*1*1*1*5=5 }}}
 
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
{{{5^6/5^4=5^((6-4))=5^2}}} and the {{{5^5/5^4=5}}} that we found can be written as {{{5=5^1=5^((5-4))}}}
{{{5^3/5^7=1/5^((7-3))=1/5^4}}} sometimes expressed as {{{5^-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*5*5*5*5/(5*5*5*5)}}} = (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*5*5*5*5/(5*5*5*5)}}} 
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 {{{(5*5*5*5*5/5)*5*5*5=5*5*5*5*5/5*5*5*5}}}