Prove that ab less than or equal to ab for all ab element of

Prove that ab less than or equal to a^b, for all a,b element of { x is an element of integers and x is greater than or equal to 2}.

Solution

given that x>=2

then

let a=2,b=2

then

ab=4, a^b=4

now

a=2,b=3

ab=6, a^b=8

now

a=3,b=3

then

ab=9,a^b=27

then by mathematical induction we can prove that

ab is either less than or equal tp a^b