Write a function elementwise$\_$array$\_$sum that computes the square of each value in list$\_1,$ the cube of each value in list$\_2,$ then returns a list containing the element$-$wise sum of these results. Assume that list$\_1$ and list$\_2$ have the same number of elements, do not use for loops.

The input parameters will both be Python lists, so you may need to convert the lists into arrays before performing your operations. The output should be a NumPy array.