Implementing a Python Program for a Custom Formula: z ( frac{x cdot y}{x cdot y^{-2}} )

To write a Python program that takes as input two integers (x) and (y) and a floating-point number (z), and outputs the result of the formula (z frac{x cdot y}{x cdot y^{-2}}), you can follow these detailed steps:

Step 1: Collect User Input

The first step is to get the values of (x), (y), and (z) from the user. This can be done using the input function in Python, where you will convert the input to the appropriate data types.

x  int(input("Enter the first integer: "))y  int(input("Enter the second integer: "))z  float(input("Enter the floating-point number: "))

Step 2: Define Variables

It's a good practice to define variables for the numerator and denominator separately to improve readability and maintainability of the code.

numerator  x * ydenominator  x * y**-2

Step 3: Handle Potential Exceptions

Ensure that the program handles exceptions such as division by zero. If either (x) or (y) is zero, the program must provide a meaningful error message or take appropriate measures to handle the situation.

if y  0:    print("Error: Division by zero is not allowed. Please enter a non-zero value for y.")else:    result  numerator / denominator    print(f"The result of the formula is: {result}")

Step 4: Explanation

Let's break down the code and the formula. The formula (z frac{x cdot y}{x cdot y^{-2}}) can be simplified as follows: The numerator is the product of (x) and (y). The denominator is the value of (x cdot y^{-2}), which is equivalent to (frac{1}{(x cdot y)^2}).

Here's the full implementation of the program:

x  int(input("Enter the first integer: "))y  int(input("Enter the second integer: "))z  float(input("Enter the floating-point number: "))numerator  x * ydenominator  x * y**-2if y  0:    print("Error: Division by zero is not allowed. Please enter a non-zero value for y.")else:    z  numerator / denominator    print(f"The result of the formula is: {z}")

In this program, we first collect the user inputs, define the variables for the numerator and denominator, handle the potential exception for division by zero, and then compute and output the result.

Conclusion

This Python program effectively implements the custom formula ( z frac{x cdot y}{x cdot y^{-2}} ). By following these steps, you can create a robust and user-friendly program that handles both input and computation with ease.