invalid_argument_for_power_function zero raised to a negative power is undefined — 2201F

Symptoms

A power() / ^ operation computed 0 raised to a negative exponent, which is undefined (division by zero). PostgreSQL raises SQLSTATE 2201F (invalid_argument_for_power_function).

• Base is 0 and the exponent is negative.
• Mathematically equivalent to 1/0.
• Common with computed base/exponent values.

What the server log shows

ERROR:  zero raised to a negative power is undefined

Why PostgreSQL raises this — what the manual says

As Section 9.3 Mathematical Functions and Operators explains:

Zero raised to a negative power is equivalent to dividing by zero, which is undefined, so power() and the ^ operator reject 0 with a negative exponent.

0 to a negative power equals 1 divided by 0 to a positive power, i.e. division by zero. Since that is undefined, PostgreSQL rejects the operation with 2201F.

Common causes

• A computed base of 0 with a negative exponent.
• Unguarded power expressions on variable inputs.
• Data that allows a zero base.

How to fix it

1. Guard against a zero base when the exponent can be negative.
2. Use CASE/NULLIF to handle the zero-base situation.
3. Validate inputs before the power operation.

Related & next steps

• SQLSTATE 2201F — Invalid Argument For Power Function (full reference)
• Message: cannot take logarithm of zero
• Glossary: Mathematical functions

Reference: PostgreSQL 18 Section 9.3 “Mathematical Functions”.