Question 183050
Here's the long way to do it:



{{{(5^2)/(5^5)}}} Start with the given expression.



{{{(5*5)/(5^5)}}} Expand {{{5^2}}} to get {{{5^2=5*5}}}



{{{(5*5)/(5*5*5*5*5)}}} Expand {{{5^5}}} to get {{{5^5=5*5*5*5*5}}} (note: there are five 5's)



{{{(highlight(5)*highlight(5))/(highlight(5)*highlight(5)*5*5*5)}}} Highlight the common terms.



{{{(cross(5)*cross(5))/(cross(5)*cross(5)*5*5*5)}}} Cancel out the common terms.



{{{1/(5*5*5)}}} Simplify



{{{1/125}}} Multiply {{{5*5*5}}} to get {{{5*5*5=5*(5*5)=5*25=125}}} 




So {{{(5^2)/(5^5)=1/125}}}



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Here's the short way to do it:



{{{(5^2)/(5^5)}}} Start with the given expression.



{{{5^(2-5)}}} Divide the terms by subtracting the exponents.



{{{5^(-3)}}} Subtract



{{{1/(5^3)}}} Flip the base to make the exponent positive.



{{{1/(5*5*5)}}} Expand {{{5^3}}} to get {{{5^3=5*5*5}}}



{{{1/125}}} Multiply {{{5*5*5}}} to get {{{5*5*5=5*(5*5)=5*25=125}}} 




So {{{(5^2)/(5^5)=1/125}}}