2.2 EXPLORE For this problem consider raising an integer a to the power n (another positive integer). Let a" express the output to this problem. 1. (2 point) Express this problem formally with input and output conditions. 2. (4 points) Describe a simple brute force algorithm to compute this product. How many multiplications does it take asymptotically in the worst case? 3. (2 point) Assume for the moment that n> and is even. Express the value of a" as a product of two subproblems. 4. (2 point) Now assume n >1 and is odd. Express the value of a" as a product of two subproblems (and possibly other terms). 5. (4 points) State a self-reduction for your problem. 6. (4 points) State a recursive algorithm that solves the problem. (2 point) State a tight asymptotic bound on the number of multiplications used by your algorithm in the worst case. 7