Question

Given non-negative integers x and n, x 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-1)th power with x
1. Write a function named power that accepts two parameters containing integer values (x and n, in that order) and recursively calculates and returns the value of x to the nth power.

Answer 1

Answer:

def power(x, n):

   if n == 0:

       return 1

   else:

       return x * power(x, n-1)

print(power(2, 3))

Explanation:

Create a function called power that takes two parameters, x and n

If n is equal to 0, return 1

Otherwise, multiply x with the function itself, but as a parameter pass x and n-1 for each iteration.

For example,

If x = 2 and n = 3,  Is 3 == 0? No, then power(2, 3) = 2 * power(2, 2)      (1)

x = 2 and n = 2, Is 2 == 0? No, then power(2, 2) = 2 * power(2, 1)          (2)

x = 2 and n = 1, Is 1 == 0? No, then power(2, 1) = 2 * power(2, 0)            (3)

x = 2 and n = 0, Is 0 == 0? Yes, power(2, 0) = 1                                       (4)

Iteration 4 will give us 1. If you substitute the power(2, 0) in iteration 3 with 1, it becomes 2. If you substitute the power(2, 1) with 2 in iteration 2, it becomes 4. If you substitute the power(2, 2) with 4 in iteration 1, it becomes 8.