Rational (Fractional) Exponents
Rational (fractional) exponents are an alternate way to express roots
Notice: The denominator of the rational exponent becomes the index of the radical, and the numerator becomes the exponent of the radicand (expression inside the radical).
We have already discussed simplifying radicals such as:
Let’s look at these two problems in a new light! When asked to simplify these radicals, it is often easier to rewrite the radicals using rational exponents and solve the problems by dealing with the laws of exponents.
Notice how applying the rules for dealing with the exponents makes quick work of the variable
Look at these examples:
When dealing with rational exponents, the Rules for Exponents are still valid!!!
Check out how these problems are done using rational exponents:
