Need solutions to the following practice problems: Let a and n be nonnegative integers. Consider the problem of calculating the nth power of a: a^n . Present a brute-force algorithm for the calculation and describe the key idea behind your solution. Determine and show the range for the number of multiplications performed overall. Develop a recursive reduce-by-one algorithm for the calculation and describe the key idea behind your solution. Establish and solve the recurrence relation for the number of multiplications performed overall. Develop a transform-and-conquer algorithm for the calculation and describe the key idea behind your transformation. Determine and show the range for the number of multiplications performed overall. Test your algorithms in Java at: http://codingbat.com/prob/p158888 Compare the results of your three solutions and assess which does more or less work. Your method should use the signature as follows (**very important: solutions should be answered in this format**): public int powerN(int base, int n) { }