Compare which of the two is greater `(100)^(1/100) and (101)^(1/101)`

Explanation

Assume f(x) `=x^(1//2)` and let us examine monotonic nature of f(x)
`f(x) =x^(1//2) .((1-enx)/(x^(2)))`
`f(x) gt0 " "rArr " " x in (0,e)`
`" and "f(x) lt0 rArr x in (e,oo)`
Hence f(x) is M.D. For `x le e`

and since `1000 lt 101`
`rArr f(100) gt f(101)`
`rArr (100)^(1//100) gt (101)^(1//100)`