A negative exponent is one preceded by a minus sign, as in 5^(-5), while a fractional exponent is one that is not a whole number, such as 5^(3/5). An exponent can be both negative and a fraction, as in the number 6^(-1/2).
A negative exponent is equivalent to the reciprocal of the of the same number taken to the opposite positive exponent. For example, 5^(-3) is equal to 1/(5^3). A fractional exponent can be solved by taking the root of the denominator to the power of the numerator. For example, 4^(2/3) is equal to the square of the cube root of 4. The root of a negative exponent with an even number in the denominator does not exist.