What is a rational exponent?

A rational exponent is an exponent written as a fraction, such as 3^1/2, which is also equal to the square root of three. With a rational exponent, the numerator indicates the power that the base number is raised to and the denominator indicates the root.

Fractional exponents are particularly useful when simultaneously raising a number to a power and taking a root. For example, raising 5^1/3 means raising 5 to the second power and taking the cube root of the result. Since raising to a power and taking a root are reciprocal operations, the order in which the operations are performed normally does not matter.