This exercise is intended to demonstrate recursive coding, the Java Math class, and exception handling.

You are to write a Java program that has at least two functions: main and recursionPower. main will be the entry point/driver and recursionPower will be a function that recursively computes the power of an integer parameter.

The maximum value that can be stored in a Java int is 2,147,483,647. As you compute powers for an integer, the values become very large very quickly and may exceed the maximum value. Oddly, in Java the basic arithmetic operations will simply overflow when that happens without any warning. A program in which that happens is allowed to continue executing with corrupted data.

However, there is a static Java class, Math, which since the advent of Java 1.8 offers a solution to that problem. (You may have already used Math with such functions as Math.abs(), Math.power(), and Math.sqrt()). The functions addExact(), subtractExact(), multiplyExact() duplicate the functions their names imply, and in addition they throw an exception if a result cause an overflow. For instance, instead of multiplying one variable by another with regular operators

a * b

you would use the Math function

Math.multiplyExact(a, b)

If the result of the multiplyExact operation is an overflow, it will throw an ArithmeticException exception.

Your program should recursively compute the powers for the range of integers 1 20 (int). You may hard-code this range. You should use the Math.multiplyExact() function for the power multiplications. If while you are computing a power and there is an overflow, handle the exception, discontinue that computation, and then proceed with the next integer in the range. You should print a clearly labeled, formatted report of your results.

ALSO (to further explain): You may pick a range (hard coded if you wish). What I want to see is some of the powers calculated for the full range of the exponent, that is the full range of recursive function calls. For some combinations, higher numbers to higher powers, the recursive calls should be forced to stop because of the overflow. You program should deal with both situations gracefully.