Show that if \(a = 1\) and \(b > 1\) then \(\mathrm { a } ^ { \mathrm { b } } < \mathrm { b } ^ { \mathrm { a } }\).
Find integer values of \(a\) and \(b\) with \(b > a > 1\) and \(\mathrm { a } ^ { \mathrm { b } }\) not greater than \(\mathrm { b } ^ { \mathrm { a } }\) (a counter example to the conjecture given in lines 7-8).