I'm getting very confused on how x^0 = 1
If we break it down exponentially and divide:
exponent of 3 = (1) * X * X * X
then to get to
exponent of 2 = (1) * X * X (dividing an X)
then to get to
exponent of 1 = (1) * X ( dividing an additional X)
THEN to get to an exponent of 0, you would be left with (1)
This makes sense.
But how does 7^0 automatically mean 1? 7^n for example is 7 to the nth power, but a power of 0 would mean 7 is multiplied by nothing, so it should still be 7(explaining where I'm currently at mentally, where my logic is hitting a wall)
What I don't understand is doing the above and going from 7^3 to 7^0 somehow automatically flips the 7^0 to a 1.
I'm assuming it has something to do with the quantity being divided by itself, but I don't get how to prove that from x^0 itself. If I was just given 7^0 and somebody told me to 'prove' 7^0 = 1, how would I do so?