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You can have an infinite number of different exponents on a base number, you would then have an infinite amount of different numbers.
The numbers called that are used in exponents can be called as a power of a number. The power or exponent can be positive , negative , zero .
Polynomial
You can use any number - rational or otherwise - as an exponent.
Yes, except for zero. Numbers larger than 1 have positive exponents, and numbers between 0 and 1 have negative exponents. Negative numbers would just have a '-' in front.