lisp programming help please

The first function is a power function that will calculate x^i
, where x can be either a real number or an
integer, but i must be an integer. In the first version, you will write this recursively, using the classic
technique that was probably used when you first saw recursion. In the second version, you will write a
function that will use a loop to construct a list containing the proper number of multiplications and then
have Lisp evaluate that.
The second function will receive a list of integers and will return a result that is a two element list
consisting of the smallest and largest values in the original list. The first version you will do will have
two helper functions that find the largest and smallest values that are used to construct the result. In the
second version, you must accomplish this task in one recursive function.
Thoughts:

The recursive power function is quite easy, but the second is a little harder. One way to accomplish
this is to have a local variable that is used to hold the list as you build it, and then use a do loop that
keeps adding the proper items to this list in the proper quantity. In other words, to calculate 53 you
could build the list (* 5 5 5) and then evaluate it.
Using helper functions to write the largest/smallest function will make that quite easy, but the nonhelper version of this problem can be quite involved. Thinking about the following might help:
• Remember that one way to accomplish a recursive function is to keep making recursive calls until
you get to the empty list and then do the real work on the way back “up.”
• If there is one element in a list, it is both the largest and the smallest.
• When the recursive function call returns, you now have a two element list with the smallest and
largest values that are in the cdr of the list. You now only need to consider how the car of the
current list might alter this result