How to perform Division of Exponents of Same Base using C#?

When dividing exponents with the same base, we use the mathematical rule: a^m ÷ a^n = a^(m-n). This means we subtract the exponent in the denominator from the exponent in the numerator while keeping the base unchanged.

In C#, we can implement this rule by subtracting the exponents and then using Math.Pow() to calculate the final result.

Mathematical Rule

The division rule for exponents with the same base is −

a^m ÷ a^n = a^(m-n)

For example: 10^10 ÷ 10^8 = 10^(10-8) = 10^2 = 100

Using Math.Pow() Method

Example

using System;

class Demo {
   static void Main() {
      double res, n, e1, e2;

      n = 10;
      e1 = 10;
      e2 = 8;

      res = e1 - e2;

      Console.WriteLine("Result = {0}^{1} : {2}", n, res, Math.Pow(n, res));
   }
}

The output of the above code is −

Result = 10^2 : 100

Using Different Base and Exponents

Example

using System;

class ExponentDivision {
   static void Main() {
      double baseValue = 5;
      double exponent1 = 7;
      double exponent2 = 3;
      
      double resultExponent = exponent1 - exponent2;
      double finalResult = Math.Pow(baseValue, resultExponent);
      
      Console.WriteLine("{0}^{1} ÷ {0}^{2} = {0}^{3}", baseValue, exponent1, exponent2, resultExponent);
      Console.WriteLine("Final Result: {0}", finalResult);
   }
}

The output of the above code is −

5^7 ÷ 5^3 = 5^4
Final Result: 625

Creating a Reusable Method

Example

using System;

class ExponentCalculator {
   static double DivideExponents(double baseValue, double exp1, double exp2) {
      double resultExponent = exp1 - exp2;
      return Math.Pow(baseValue, resultExponent);
   }
   
   static void Main() {
      double result1 = DivideExponents(2, 8, 3);
      double result2 = DivideExponents(3, 6, 2);
      double result3 = DivideExponents(10, 5, 2);
      
      Console.WriteLine("2^8 ÷ 2^3 = 2^5 = {0}", result1);
      Console.WriteLine("3^6 ÷ 3^2 = 3^4 = {0}", result2);
      Console.WriteLine("10^5 ÷ 10^2 = 10^3 = {0}", result3);
   }
}

The output of the above code is −

2^8 ÷ 2^3 = 2^5 = 32
3^6 ÷ 3^2 = 3^4 = 81
10^5 ÷ 10^2 = 10^3 = 1000

Conclusion

Division of exponents with the same base follows the simple rule of subtracting the exponents: a^m ÷ a^n = a^(m-n). In C#, implement this by subtracting the exponents and using Math.Pow() to calculate the final result.