\({\left( {\dfrac{{\sqrt 2 }}{2}} \right)^m} < {\left( {\dfrac{{\sqrt 3 }}{2}} \right)^m}\)     

\({\left( {\dfrac{{\sqrt 2 }}{2}} \right)^m} > {\left( {\dfrac{{\sqrt 3 }}{2}} \right)^m}\)     

\(1 < {\left( {\dfrac{{\sqrt 2 }}{2}} \right)^m} < {\left( {\dfrac{{\sqrt 3 }}{2}} \right)^m}\)           

\({\left( {\dfrac{{\sqrt 2 }}{2}} \right)^m} > {\left( {\dfrac{{\sqrt 3 }}{2}} \right)^m} > 1\)