The answer could not use  or any power of 3, 5, 6, or 8 higher than the
power 2, since that would result in a value over 100 even before adding c.

So the value of the first term  could at most be one of these

, , , , or 

So the most we could get for  is 64.  So the answer is between using
 and .  However if we used  for the 64, the largest number 8 
would not be available for c to add to it, whereas if we use , we can
add the largest number 8 to that.  Thus the answer is:

 

Edwin