I think you mean [tex]\frac{5^{-1}}{5^0}[/tex]
ok, know some stuff
[tex]x^0=1[/tex] for all real values of x
[tex]x^{-m}=\frac{1}{x^m}[/tex]
so
[tex]\frac{5^{-1}}{5^0}=[/tex]
[tex]\frac{\frac{1}{5^1}}{5^0}=[/tex]
[tex]\frac{\frac{1}{5}}{5^0}=[/tex]
[tex]\frac{\frac{1}{5}}{1}=[/tex]
[tex]\frac{1}{5}[/tex]
it results in 1/5
or, we could have done
[tex]\frac{x^m}{x^n}=x^{m-n}[/tex] and
[tex]x^{-m}=\frac{1}{x^m}[/tex]
so
[tex]\frac{5^{-1}}{5^0}=5^{-1-0}=5^{-1}=\frac{1}{5^1}=\frac{1}{5}[/tex]
the result is [tex]\frac{1}{5}[/tex]
