The power conjunction has the obvious use of applying a verb repeatedly. Thus, if double=.+: , then double 3 is 6.  We can use the power conjunction to specify an arbitrary number of applications:

   thrice=.^:3:
   double thrice 5
40

The number of times a verb is to be applied can be zero. This suggests a way to apply a verb conditionally.

   reverse=.|.
   if=.^:
   tlh=.{:<{. NB. tail less than head
   reverse if tlh 4 0 1 3 2
2 3 1 0 4
   reverse if tlh 2 1 0 3 4
2 1 0 3 4
   
   halve=.-:
   even=.-.@(2:|]) NB. not 2 residue
   halve if even 19
19
   halve if even 160
80