why does 0 to the power of 0 equal 1?
In: 97
0⁰ is undefined. That doesn’t mean it can’t have a value, it means there isn’t enough info to determine based on that alone. Let me give you an example. If you’re familiar with limits, this may be a bit tedious for you. So skip ahead as needed.
Let’s take the limit as x approaches 0 of 0^(x) this means we look at the value of the expression as x gets closer and closer to 0 (meaning the expression gets closer and closer to 0⁰) at x=0.1 the expression is 0^(0.1) which is 0 at x=0.01, the expression is 0^(0.01) which is also 0 and at x=0.0000001 it’s 0^(0.0000001) which is also 0. The limit is 0 because this pattern holds for any x arbitrarily close to 0. Therefore 0⁰ can equal 0
Let’s take the limit as x approaches 0 of x^(0) this means we look at the value of the expression as x gets closer and closer to 0 (meaning the expression gets closer and closer to 0⁰) at x=0.1 the expression is 0.1^(0) which is 1 at x=0.01, the expression is 0.01^(0) which is also 1 and at x=0.0000001 it’s 0.0000001^(0) which is also 1. The limit is 1 because this pattern holds for any x arbitrarily close to 0. Therefore 0⁰ can equal 1
By changing how we approach 0⁰, we can make it equal many different things.
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