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What are the alternatives?

A. Less than 0,

B. 0

C. between 0 and 1,

D 1.

A base less than 0 runs into all sorts of difficulties with fractional powers, such as square roots. Best avoided until you are an expert in complex numbers.

The Base of 0 and 1 are not particularly helpful. 0 to any positive exponent is 0 and to any negative exponent is undefined. 1 is not much better, since 1 raised to any power is 1 and that would not take you very far.

The base could be between 0 and 1, but that would be the same as using its reciprocal as the base and switching the signs on the exponents. It is intuitively simpler to have the base greater than 1 so that the bigger the power, the bigger the number.

So, although C is possible, it has not advantage over using a base greater than 1.

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12y ago

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Q: Why the value of index of base is greater than 1?
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