# Recursive Powers Exercise

### Objective

To practice writing recursive functions.

For this lab, you will write a program to read in two integers from the user, $base$, and $exponent$, calculate the value of $base^{exponent}$ and print this value to the screen. To do this, you will write two recursive functions:

1. The first will get a positive number from the user. If the user enters a number less than or equal to 0, it should keep recursing until the number is positive.
2. The second will compute the power using the following recursive formula:

$X^Y = \begin{cases} X^{(Y/2)} \cdot X^{(Y/2)}, \hfill & \text{ if Y is even} \\ X^{(Y/2)} \cdot X^{(Y/2)} \cdot X, \hfill & \text{ if Y is odd} \\ \end{cases}$

You will have to add a base case to the function so that it will eventually bottom out and return a value directly.

This method of computing powers is actually more efficient than the straightforward loop solution of looping $exponent$ times and multiplying $base$ that many times!

Remember, this program can only use recursion, it should have no loops at at all!

The main function should simply call the function to get input two times, then pass those values to the power function, printing the output.

### Example Run

Below is an example run of this program:

\$ ./powers
Enter a positive number: 0
I said a positive number!
Enter a positive number: 3
Enter a positive number: -4
I said a positive number!
Enter a positive number: 4
81


### Submitting

When you're done, email the code to ifinlay@umw.edu.