 # Python Program to Compute x^n/n!

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Factorial:

The product of all positive integers less than or equal to n is the factorial of a non-negative integer n, denoted by n! in mathematics:

n! = n * (n – 1) *(n – 2) * . . . . . . . . . . 3 * 2 * 1.

5 != 5* 4 * 3 * 2 *1= 120

Given the values of x, n and the task is to calculate the value of x^n/n!

Examples:

Example1:

Input:

Given Number = 3
Given x value =  6

Output:

The value of x^n/n! with the given n,x { 3 6 } values= 36.0

Example2:

Input:

Given Number = 5
Given x value = 8

Output:

The value of x^n/n! with the given n,x { 5 8 } values= 273.06666666666666

## Program to Compute x^n/n! in Python

Below are the ways to calculate the value of x^n/n! :

### Method #1: Using For Loop (Static Input)

Approach:

• Give the number as static input and store it in a variable.
• Give the value of x as static input and store it in another variable.
• Take a variable, initialize it with the value ‘1’, and store it in another variable say ‘factorl‘.
• Loop from 1 to the given number using the for loop.
• Inside the loop, calculate the factorial of a given number by multiplying the value of the above variable “factorl” with the iterator value.
• Store it in the same variable ‘factorl‘.
• Calculate the value of x^n/n! using the pow() function and store it in another variable.
• Print the value of  x^n/n! for the given n, x values.
• The Exit of the Program.

Below is the implementation:

# Give the number as static input and store it in a variable.
gvn_n_val = 3
# Give the value of x as static input and store it in another variable.
gvn_x_val = 6
# Take a variable, initialize it with the value '1', and store it in another variable say
# 'factorl'.
factorl = 1
# Loop from 1 to the given number using the for loop.
for itr in range(1, gvn_n_val+1):
# Inside the loop, calculate the factorial of a given number by multiplying the value of
# the above variable "factorl" with the iterator value.
# Store it in the same variable 'factorl'.
factorl *= itr
# Calculate the value of x^n/n! using the pow() function and store it in another variable.
fnl_reslt = pow(gvn_x_val, gvn_n_val)/factorl
# Print the value of  x^n/n! for the given n, x values.
print("The value of x^n/n! with the given n,x {",
gvn_n_val, gvn_x_val, "} values=", fnl_reslt)


Output:

The value of x^n/n! with the given n,x { 3 6 } values= 36.0

### Method #2: Using For loop (User Input)

Approach:

• Give the number as user input using the int(input()) function and store it in a variable.
• Give the value of x as user input using the int(input()) function and store it in another variable.
• Take a variable, initialize it with the value ‘1’, and store it in another variable say ‘factorl‘.
• Loop from 1 to the given number using the for loop.
• Inside the loop, calculate the factorial of a given number by multiplying the value of the above variable “factorl” with the iterator value.
• Store it in the same variable ‘factorl‘.
• Calculate the value of x^n/n! using the pow() function and store it in another variable.
• Print the value of  x^n/n! for the given n, x values.
• The Exit of the Program.

Below is the implementation:

# Give the number as user input using the int(input()) function and
# store it in a variable.
gvn_n_val = int(input("Enter some random Number= "))
# Give the value of x as user input using the int(input()) function and
# store it in another variable.
gvn_x_val = int(input("Enter some random Number= "))
# Take a variable, initialize it with the value '1', and store it in another variable say
# 'factorl'.
factorl = 1
# Loop from 1 to the given number using the for loop.
for itr in range(1, gvn_n_val+1):
# Inside the loop, calculate the factorial of a given number by multiplying the value of
# the above variable "factorl" with the iterator value.
# Store it in the same variable 'factorl'.
factorl *= itr
# Calculate the value of x^n/n! using the pow() function and store it in another variable.
fnl_reslt = pow(gvn_x_val, gvn_n_val)/factorl
# Print the value of  x^n/n! for the given n, x values.
print("The value of x^n/n! with the given n,x {",
gvn_n_val, gvn_x_val, "} values=", fnl_reslt)


Output:

Enter some random Number= 2
Enter some random Number= 10
The value of x^n/n! with the given n,x { 2 10 } values= 50.0

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