Definition of : (This is read as to the one-half power.) If the laws of exponents are to hold, then . Since the square of is , is defined to be .
OTHER FRACTIONAL POWERS
Definition of is defined to be , since its cube is .
Definition of is defined to be , since is .
Definition of : Using the Power of a Power Law of Exponents in either of two ways:
Therefore, is defined to be either of the equivalent expressions or .
The definition of any rational exponent is:
If and are integers, and is a positive real number, then
CUBE ROOTS AND OTHER RADICALS
Fractional exponents can also be written as radicals: