Rational = Fraction
What does it mean to have a fraction in the exponent?
We know the are of a square is , in this case length and width are the same, so . To find out the length we need to use the inverse operation, the squareroot. So
This makes sense because
(or they’re both the same.)
Using our properties of exponents we can see that if we write
since we add the exponents. From here we learn that
Having a fraction in the exponent is called a RATIONAL EXPONENT. A rational exponent is just another way to write a root.