W1 Using our rules for Hoare logic, prove the correctness of the following program that computes the integer nth power of integer x. Although vou might want to figure out the proof using tree layout, give your solution in linear form similar to the proofs of division given in the textbook. We give the initial assumption (n ? 0} and final goal in the program below: // Slow Exponentiation :T while (k>0) do done Bonus points Why is this called slow exponentiation? To get one bonus point, give code that is exponentially faster in n, and to get the second bonus point, argue convincingly that vour speedup is exponential. W1 Using our rules for Hoare logic, prove the correctness of the following program that computes the integer nth power of integer x. Although vou might want to figure out the proof using tree layout, give your solution in linear form similar to the proofs of division given in the textbook. We give the initial assumption (n ? 0} and final goal in the program below: // Slow Exponentiation :T while (k>0) do done Bonus points Why is this called slow exponentiation? To get one bonus point, give code that is exponentially faster in n, and to get the second bonus point, argue convincingly that vour speedup is exponential