Square and Cube Roots as Exponents
We define a1/2 as the non-negative number such that when you square it, you get a.
91/2 = 3
We define a1/3 as the number such that when you cube it you get a.
81/3 = 2
We define a1/n as the unique non-negative number x such that
xn = a
If n is odd then the domain of the function f(x) = x1/n is all real numbers and if n is even then the domain of f(x) = x1/n is all non-negative numbers.
Which are real numbers:
We define xm/n by (x1/n)m
82/3 = (81/3)2 = 22 = 4
In Radical notation the above can be written as:
Rules of Exponents
x1/3 y -2/5
= x1y -8/20 - 5/20 = x y -13/20