Compute the product a * b² * c³ ... efficiently

I absolutely don't know if this is the optimal approach (although I think it is asymptotically optimal), but you can do it all in O(N) multiplications. You group the arguments of a * b^2 * c^3 like this: c * (c*b) * (c*b*a). In pseudocode:

result = 1
accum = 1
for i in 0 .. arguments:
  accum = accum * arg[n-i]
  result = result * accum

I think it is asymptotically optimal, because you have to use N-1 multiplications just to multiply N input arguments.