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Look at this sequence:

103 = 1000

102 = 100

101 = 10

100 = 1


On the left side, the exponent reduces by one at a time; on the right side, the number decreases by a factor 10. So, the last step, 10 to the power zero = 1, is quite logical.


Note that this doesn't PROVE anything; in fact, the definition "x to the power zero = 1" might be considered an arbitrary definition. The sequence above only shows that the definition makes sense.

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