Sure. It may not be very useful to use 1 but any number is eligible to be an exponent.
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no exponent can make a number equal to zero, however any number with an exponent of zero is one.
Not sure what you're asking. Any number can be an exponent, like 1013, where 13 would be the exponent in this case. If you were given the number 13, and asked what the exponent was, the answer would be one (1), since any number to the 1 power equals that number, so 131 = 13, if no exponent is given then it is assumed to be one (1).
24: the number of digits is always one more than the exponent of 10 if the exponent is positive.
A number to a negative exponent is the inverse of the number to the positive exponent. That is, x-a = 1/xa
no it equals one no matter the number