The exponents must be non-negative integers.
Examples:
\(x\) is a polynomial (degree 1)
\(x^2-1\) is a polynomial (degree 2)
\(x^3-\dfrac1{x^3}=x^3-x^{-3}\) is NOT a polynomial, but a rational expression
\(\sqrt x=x^{1/2}\) is NOT a polynomial, but an algebraic expression.