Power of a Number

In this lesson, we will learn how to find the power of a number using recursion.

We'll cover the following

What does “Power of a Number” mean?

The power (or exponent) aa, of a number xx represents the number of times xx needs to be multiplied by itself. It is written as a small number to the right and above the base number.

For example, if the base number is 22 and the exponent value is 33, we represent this as follows:

23=82^3 = 8 ​

The following illustration explains the concept.

Power of a number
Power of a number

To code this problem recursively we need to break it down. In each step, we are multiplying the number with itself.

Implementation

Let’s have a look at the code:

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def power(base, exponent):
  # Base Case
  if exponent == 0 :
    return 1
    
  # Recursive Case
  else :
    return base * power(base, exponent - 1);
# Driver Code
print(power(2, 3))

Explanation

In the code above, the function, power(), is a recursive function as it makes a recursive call to another instance of itself.

In recursion, the final solution comprises of solutions to subtasks.

For example:

23=2∗222^3 = 2 * 2^2

23=2∗(2∗21)2^3 = 2 * (2 * 2^1)

Therefore we can generalize this as follows:

xa=x∗(x)a−1x^a = x * (x)^{a-1}

(x)a−1=x∗(x)a−2(x)^{a-1} = x * (x)^{a-2}

(x)a−2=x∗(x)a−3(x)^{a-2} = x * (x)^{a-3}

.

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(x)a−a=1(x)^{a-a} = 1

This can then be mapped as a recursive function. The last condition (x)a−a=(x)0=1(x)^{a-a} = (x)^{0} = 1 will be our base case. While all the rest can be written in the generic format: xa=x∗(x)a−1x^a = x * (x)^{a-1}

Let’s have a look at an illustration to better visualize what is going on in the code.

In the next lesson, we will have a look at another example of solving problem with recursion.