Zero and Negative Indices

Zero Index

Any non-zero number to the power 0 equals 1.

a⁰ = 1 (where a ≠ 0)

Example: 7⁰ = 1, (3x)⁰ = 1.

Negative Index

A negative index means “one over” (reciprocal).

a^-n = 1/aⁿ

Example: 2^-3 = 1/2³ = 1/8.

Example: 1/x^-4 = x⁴.

Common mistake: x^-2 is not a negative number, it is 1/x².

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