Question

why x to the power 0 = 1​

Answer 1

Answer:

because when power is 0 we considered x + 0 = 1

Answer 2

Answer:

x⁰ = 1 is a identity & it's true for x ∈ ℝ - {0}

Proof :

x ⁰ = x ⁿ⁻ⁿ

There is an identity

x ⁿ⁻ⁱ = xⁿ / xⁱ for all values of x except 0 because 0ⁿ / 0ⁱ is undefined

x ⁰ = x ⁿ⁻ⁿ = xⁿ / xⁿ

There's an identity

k / k = 1 for all values of k except 0

x⁰ = x ⁿ⁻ⁿ = xⁿ / xⁿ = 1 for x ∈ ℝ - {0}

Hence Proved.