(a) Give a recursive algorithm whose input is a real number r and a non-negative integer n, and whose output is r^(2^n).Note that the exponent of r is 2^n.Your algorithm should only use addition and multiplication operations and should not contain any loops.

(b) Use induction to prove that your algorithm to compute r^(2^n)returns the correct value for every input pair (r, n), where r is a real number and n is a non-negative integer.