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Answer:
The zero exponent rule basically says that any base with an exponent of zero is equal to one. For example: x^0 = 1. 5^0 = 1
So, the reason that any number to the zero power is one is because any number to the zero power is just the product of no numbers at all, which is the multiplicative identity, 1.
The negative sign on an exponent means the reciprocal. Think of it this way: just as a positive exponent means repeated multiplication by the base, a negative exponent means repeated division by the base. So 2^(-4) = 1/(2^4) = 1/(2*2*2*2) = 1/16. The answer is 1/16.
Rational exponents (also called fractional exponents) are expressions with exponents that are rational numbers (as opposed to integers ). While all the standard rules of exponents apply, it is helpful to think about rational exponents carefully.