Rational (Fractional) Exponents

Let's start with looking at the rule for rational exponents:

Now let's practice with a few numerical expressions.

A little more challenging

write as a radical and simplify

expand using prime factorization

group triples because


Now let's practice with a few variable expressions.

This is a little more challenging because the numerator is larger than the denominator.

  • write as a radical expression

  • =

  • =

    group triples and you still have x2

    under the radical

An easy way to remember the rule is to choose an example that you know for sure. For example. This way you can remember that the denominator is the number that goes with the radical and the numerator goes with the number/variable under the radical.

Reminder: the exponent rules do not change when you are multiplying, dividing or raising a power to a power just because the exponent is a fraction.

Related Links:
Exponents and Powers
The Laws of Exponents
Integers as Exponents
Evaluate Exponents
Evaluate integers with exponents
Positive and Negative Integer Exponents
Rational (Fractional) Exponents
Zero Exponents
Dependent and Independent Variables

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