Power of a number in Python without pow()

Python already has ** and pow() for powers: 2 ** 10 is 1024. Writing the calculation yourself shows what a power means: 2¹⁰ is 2 multiplied by itself 10 times.

The program

def power(base, exponent):
    result = 1
    for _ in range(abs(exponent)):
        result *= base
    if exponent < 0:
        return 1 / result
    return result


print(power(2, 10))
print(power(3, 4))
print(power(5, 0))
print(power(2, -3))

1024
81
1
0.125

How it works

• result starts at 1 and is multiplied by base once for each step of the loop.
• Any number to the power 0 is 1. With exponent = 0 the loop does not run, so the function returns 1.
• A negative exponent means "1 divided by the positive power": 2⁻³ = 1 / 2³ = 1/8 = 0.125. The loop uses abs(exponent), and the division happens at the end.
• power(0, -1) raises a ZeroDivisionError, which is correct: 1 / 0 has no value. Python's 0 ** -1 does the same.

Another way: exponentiation by squaring

The loop above needs 1,000 multiplications for an exponent of 1,000. Exponentiation by squaring needs only about 20. It uses the fact that x¹⁰ = (x²)⁵, so it squares the base and halves the exponent at each step:

def fast_power(base, exponent):
    result = 1
    while exponent > 0:
        if exponent % 2 == 1:
            result *= base
        base *= base
        exponent //= 2
    return result


print(fast_power(2, 10))
print(fast_power(3, 200) == 3 ** 200)

1024
True

• When the exponent is odd, one copy of base goes into result, so the rest has an even exponent.
• base *= base squares the base and exponent //= 2 halves the exponent.
• This version is for exponents of 0 or more. Python's own ** uses the same idea for whole numbers.