>   NB. x u&n y ↔ u&n^:x y
>  That part is good.
>
>  How can you get from there to the power rule?
>   NB. x u^:n y ↔ x&u^:n y

You don't need to; you're already done.  To wit:
  
   3 (%&2) 13
   (%&2)^:(3) 13
   (%&2) (%&2) (%&2) 13

   (%&2) (%&2) (13 % 2)
   (%&2)  ((13 % 2) % 2)
   ((13 % 2) % 2) % 2
 
No need for more rules.  

-Dan


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