Python pow(): Calculate Exponentiation and Modulo Power

The pow() function calculates the power of a number (base ** exponent) efficiently. It also supports an optional modulo operation, making it useful for cryptography, mathematical calculations, and performance optimizations.

Example

print(pow(2, 3))  
# Output: 8  (2³ = 8)

This raises 2 to the power of 3.

Syntax

pow(base, exponent, mod=None)

• base → The number to raise.
• exponent → The power to raise it to.
• mod (optional) → A number for modulo operation ((base ** exponent) % mod).
• Returns → The result of the exponentiation, optionally modded.

1. Calculating Power

print(pow(5, 3))  
# Output: 125 (5³ = 125)

Same as 5 ** 3.

2. Using pow() with Modulo

print(pow(5, 3, 7))  
# Output: 6  (5³ % 7 = 125 % 7 = 6)

This computes efficiently for large numbers.

3. Using pow() with Negative Exponents

print(pow(2, -3))  
# Output: 0.125 (2⁻³ = 1/8)

Same as 1 / (2 ** 3).

4. Faster Modulo for Cryptography

print(pow(3, 200, 13))  
# Output: 9 (Huge exponent handled efficiently)

Useful in RSA encryption and modular arithmetic.

5. Comparing pow() with ** Operator

print(2 ** 10)  # Output: 1024
print(pow(2, 10))  # Output: 1024

Both give the same result, but pow() is faster for modulo calculations.

Key Notes

• ✔ Calculates exponents (base ** exponent) efficiently.
• ✔ Supports modulo operation for optimized performance.
• ✔ Works with negative exponents.
• ✔ Great for cryptography and large numbers.

By using pow(), you can perform fast exponentiation, optimize calculations, and work with modular arithmetic. 🚀