why does 0 to the power of 0 equal 1?
In: 97
Let’s start by showing aything raised to the power of 0 is equal to 1 under the following logic.
When you divide like bases raised to an exponent, you subtract the exponent. Like so
A^b / A^c = A^b-c. So what if you divide like base and like exponent?
A^b / A^b = A^b-b
b-b is equal to 0, but also, any expression divided by itself is 1. So A^b / A^b is equal to A^0, but it’s also equal to 1. Therefore, anything (A) raised to the 0th power is 1.
However, 0 is an exception, because following the logic above, 0^0 is the product of 0^b / 0^b resulting 0/0 which is undefined.
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