This exact question is on a puzzle worksheet over rational exponents used by teachers. The answer to the puzzle is Nicole Oresme.
The laws of exponents work the same with rational exponents, the difference being they use fractions not integers.
You can use any number - rational or otherwise - as an exponent.
In terms of mathematical concepts, there is no difference at all. In practical terms, some rational exponents or rational number will result in rational answers while radical exponent won't. But that is hardly a significant difference.
YES
Rational exponents are exponents that are fractions or decimals. They are related to integer exponents because they represent a different way of expressing the same mathematical operation. For example, an integer exponent of 2 represents squaring a number, while a rational exponent of 1/2 represents taking the square root of a number.
A rational exponent is an exponent in the form of a fraction. Many financial formulas use rational exponents. Compound interest is formula that uses rational exponents.
The laws of exponents work the same with rational exponents, the difference being they use fractions not integers.
You can use any number - rational or otherwise - as an exponent.
What Is an Exponent, Anyway? There
In terms of mathematical concepts, there is no difference at all. In practical terms, some rational exponents or rational number will result in rational answers while radical exponent won't. But that is hardly a significant difference.
That they can have any value: integer, rational, irrational or complex.