Question

17.8.1: Writing a recursive math function. Write code to complete raise_to_power(). Note: This example is for practicing recursion; a non-recursive function, or using the built-in function math.pow(), would be more common.

Answer 1

To write a recursive function that raises a number to a power, define a function that multiplies the base with a reduced power in each recursive call until reaching a base case. This function exemplifies a core concept in computer science, useful for various mathematical applications.

Step-by-step explanation:

Writing a Recursive Math Function

Raising a number to a power, such as executing 4³, is a process of multiplying the number (base) by itself repeatedly for the number of times indicated by the power (exponent). In recursive function writing, the function calls itself with a reduced exponent until it reaches the base case, usually an exponent of 0 or 1. Recursive functions are a key concept in computer science and can be used to solve problems such as exponentiation elegantly. Here is a sample Python function for raising a number to an integer power:

def raise_to_power(base, exponent):
if exponent == 0:
return 1
elif exponent == 1:
return base
else:
return base * raise_to_power(base, exponent - 1)

Understanding this concept is essential for tasks like converting values between units raised to powers of 10 or solving for variables in equations such as the Pythagorean Theorem. Remember that multiplication of exponents (e.g., (a⁴)⁵ = a¹⁹) corresponds to the repeated application of the base, a concept reflected in the recursive structure.