Question

Programming Langauge: Java

•Given non-negative integers x and n, x taken to the nth power can be defined as:

•x to the 0th power is 1

•x to the nth power can be obtained by multiplying x to the n-1th power with x

•Write a long-valued method named power that accepts an two int parameters x and n (in that order) and recursively calculates and returns the value of x taken to the n'th power

•For example, to find x4

•x4 = x * x3

•x3 = x * x2

•x2 = x * x1

•x1 = x

•x0 = 1

•Next write the code to compute powers using iteration

Answer 1

I have uploaded the Images of the code, Typed code and Output of the Code. I have provided explanation using comments (read them for better understanding).

Images of the Code:
Note: If the below code is missing indentation please refer code Images

Typed Code:

// importing required packages
import java.util.*;

// A Main class
public class Main
{
// A long valued method named as power
// with input parameters x and n (Non negative numbers)
static long power(int x, int n)
{
// checking whether x or n are negative
if( x<0 || n<0)
{
// returning 0
return 0;
}
else
{
// if n is 0
if(n == 0)
{
// returning value 1
return 1;
}
else
{
// calling method power with parameters x,n-1
// and returning x and power(x,n-1)
return x*power(x, n-1);
}
}
}
  
// Main Method
   public static void main(String[] args)
   {
   // local variables
   int x=5, n=3;
  
   // calling the Method power and printing the returned value
       System.out.print(x + "^" + n + " = " + power(x,n));
       System.out.println(" (using recursion method power)");
      
       // A variable to store power value
       long power=1;
      
       // printing informative message
       System.out.print(x + "^" + n + " = ");
      
       // calculating power using iterations
       // A while loop that runs until n becomes 0
       while(n>0)
       {
       // multiplying value of x with power
       power = power * x;
       // decrementing n
       n--;
       }
       // printing calculated power
       System.out.print(power);
       // printing the message
       System.out.println(" (using iteration)");
      
   }
}
//code ended here

Output:

If You Have Any Doubts. Please Ask Using Comments.

Have A Great Day!