Write the definition of a function that takes as input the three numbers. The function returns true if the first number to the power of the second number equals the third number; otherwise, it returns false. (Assume that the three numbers are of type double.)

I am writing a C++ program.

Here is the function CheckPower() which is a bool return type function which means it will return either true of false. This function has three double type parameters. This function returns true if the first number to the power of the second number equals the third number; otherwise, it returns false.

bool CheckPower(double number1, double number2, double number3)

{

   double power; // stores value of number1 to the power number2

   power = pow(number1,number2); // pow() function to computer power

   if (power==number3) // if the value of power is equal to third no number3

       return true; // returns true

   else // if above condition evaluate to false then returns false

       return false;

}

Explanation:

Lets take the values of number1 = 3, number2 = 2 and number3 = 9 to understand the above function.

The pow() function is a power function to calculate the result of number1 raised to the power of number2. Here number1 is the base number and number2 is exponent number. As number1 = 3 and number2 = 2 so this is equivalent to 3² . So 3 raise to the power 2 is 9. The value stored in power is 9.

power = 9

Next, the if condition checks if the value in power is equal to the value of number3. The value of number3 is 9 and the value in power variable is also 9 so the If condition evaluates to true. So the if part is executed which returns true.

If the value of number3 is, lets say, 10 then the If condition evaluates false as the value of power is not equal to value of number3. So the else part is executed which returns false.

If you want to see the output of this function you can write a main() function as following:

int main()

{   double num1, num2, num3;

   cout << "enter first number: ";

   cin >> num1;

   cout << "enter second number: ";

   cin >> num2;

   cout << "enter third number: ";

   cin >> num3;

   if(CheckPower(num1, num2, num3))

   { cout<<"True";    }

   else

   { cout<<"False";  }    }

This is a main() function which asks the user to enter the values of three numbers num1, num2 and num3. The if condition calls CheckPower() function to check if the first number to the power of the second number equals the third number. If this condition evaluates to true, the message True is displayed on the screen otherwise message False is displayed on output screen.

The screen shot of program along with its output is attached.