That is the way it is defined; in theory, it could be defined any other way. But the definition commonly used makes several rules maintain their validity, for example, the law about adding exponents - even when the exponent is negative.

Consider this sequence:

103 = 1000

102 = 100

101 = 10

100 = 1

10-1 = 1/10

10-2 = 1/100

Every time the exponent is reduced by one, the result gets reduced by a factor of 10. So, it seems logical to continue this pattern for a zero or negative exponent. Mind you, this is no proof - after all, the negative exponents is a matter of definitions, not of proof. The above only merely shows that the definition is reasonable.

That is the way it is defined; in theory, it could be defined any other way. But the definition commonly used makes several rules maintain their validity, for example, the law about adding exponents - even when the exponent is negative.

Consider this sequence:

103 = 1000

102 = 100

101 = 10

100 = 1

10-1 = 1/10

10-2 = 1/100

Consider this sequence:

103 = 1000

102 = 100

101 = 10

100 = 1

10-1 = 1/10

10-2 = 1/100

Consider this sequence:

103 = 1000

102 = 100

101 = 10

100 = 1

10-1 = 1/10

10-2 = 1/100

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