Recursive computation of number x raised to the power of n, $$ x^n$$ where $$ n \geq 0 $$

Power(X,N)
1 if N < 0 return Error(n>=0 is expected)
2 if N = 0 result = 1
3 else
4 if N > 0 result = X * Power(X,N-1)

We can raise a number to a power by repeatedly multiplying that number by itself. So if we know $$x^k$$ we can get $$ {x} ^ NaN$$ by multiplying $$x^k$$ by x. The recursive definition is $$x^k = x * x ^ NaN$$ This gives us the recursive case. The base case is $$ {x} ^ 0 $$ = 1 as any number raised to power 0 is 1.

JAVA IMPLEMENTATION

import java.util.Scanner;

/**
 * Created by Ganesh.r.hegde on 16-Feb-18.
 */
public class RecursivePower {

    public static void main(String[] args) {

        System.out.println("Please enter the number :");

        Scanner scanner = new Scanner(System.in);

        int number = scanner.nextInt();

        System.out.println("Please enter the positive exponent :");

         int exp = scanner.nextInt();

         if(exp < 0)
             throw new IllegalArgumentException("Please enter positive exponent");
          else
         {
             System.out.println(number + " to the power of "+exp +" is "+powers(number,exp));
         }
   }


    /** Recursive power method
     pre: n >= 0
     @param x The number being raised to a power
     @param n The exponent
     @return x raised to the power n
     */
    public static double powers(double x, int n) {
        if (n == 0)
            return 1;
        else
            return x * powers(x,n-1);
    }

}