Definition of b1/2: (This is read as b to the one-half power.) If the laws of exponents are to hold, then . Since the square of b1/2 is b, b1/2 is defined to be .
Definition of b1/3: b1/3 is defined to be , since its cube is b.
Definition of b1/4: b1/4 is defined to be , since (b1/4)4 is b.
Definition of b3/4: Using the Power of a Power Law of Exponents in either of two ways:
Therefore, b3/4 is defined to be either of the equivalent expressions .
The definition of any rational exponent is:
If p and q are integers, q ≠ 0 and b is a positive real number, then
Fractional exponents can also be written as radicals: