posted by C .
Is this a true statement?
Polynomials and radical expressions differ because radical expressions contain rational numbers as exponents and polynomials do not.
I think you have it backwards, with some additonal miconceptions.
Polynomials have rational (and, in fact, integer) exponents.
Radical expressions contain variables to fractional powers. A square root corresponds to an exponent of 1/2. That is still a rational number.