The difference between exponential and radical is:
Exponential: The way to write the integer times a number is multiplied by itself.
Example:
[tex]a^3=a\cdot a\cdot a[/tex]Radical: The way to write the non-integer (fractional) times a number is multiplied by itself.
example:
[tex]a^{\frac{1}{3}}=\sqrt[3]{a}[/tex]