SOLUTION: why does any base to the zero power = 1

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Question 73649: why does any base to the zero power = 1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
When you say x%5E2=x%2Ax you're saying that you're multiplying 2 x's. When you go from x%5E2 to x%5E3 you're going to multiply x by x%5E2 (ie x%2Ax%5E2=x%5E3. To undo this, you divide. So if I go from x^3 to x^2, I'm saying x%5E3%2Fx=x%2Ax%2Across%28x%29%2Fcross%28x%29 and I get x^2. So in a sense this applies x%5Ea%2Fx%5Eb=x%5E%28a-b%29, with the example showing why it's true. So if I go from x^1 (which is x) to x^0 I would do this:
x%5E0=x%5E%281-1%29=x%5E1%2Fx%5E1=x%2Fx=1and it will hold true for any x. Hope this makes sense.