Zero Index

Zero Index Law

The zero index law states that anything (except zero) to the power of zero is 1.

a⁰ = 1, a ≠ 0

Q1) Should 0⁰ = 1? Why?

Argument for YES

In the fringe case of the binomial expansion of (a + 0)ⁿ , the first term will be aⁿ0⁰ which implies that 0⁰ has to be 1.
When you consider the limit for x^xas x tends to 0, the limit tends to 1.

Argument for NO

When you consider the limit for 0^xas x tends to 0, the limit tends to 0. Different approaches to 0⁰using different limits results in differing answers hence 0⁰is indeterminate.

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