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Two ways of looking at it. First is the law of adding exponents when you multiply terms. For example, 2^4 is 16, whereas 2^-4 is 1/16. Multiplying 2^4 by 2^-4 gives 2^0 when you add the exponents. But multiplying 16 by 1/16 gives 1. So 2^0 has to be 1. Another way is pattern matching. 3 to the power of 3 = 27. 3 to the power of 2 = 9. 3 to the power of 1 = 3. 3 to the power of 0 = ____ 3 to the power of –1 is 1/3. 3 to the power of –2 is 1/9. 3 to the power of –3 is 1/27. What goes in the blank ? Well follow the pattern. Every number on the right is the preivous number divided by 3. So it has to be 1. Even 0^0 is defined to be 1 and not 0.

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Q: Why is the power of zero always 1?

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Any number except 0 itself raised to the power of zero exponent is always equal to 1

Because any number raised to the power of zero always equals one as for example 666^0 = 1

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Because any number raised to the power of 0 is always equal to 1

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