1. In other words, exponents that are fractions.
Rational Exponents
In other words, exponents that are fractions.

2. Definition of For any real number b and any integer n > 1,
except when b < 0 and n is even

3. Examples:

4. Examples:

5. Definition of Rational Exponents
For any nonzero number b and any integers m and n with n > 1,
except when b < 0 and n is even

6. NOTE: There are 3 different ways to write a rational exponent

7. Examples:

8. Simplifying Expressions
No negative exponents
No fractional exponents in the denominator
No complex fractions (fraction within a fraction)
The index of any remaining radical is the least possible number

9. Get a common denominator - this is going to be our index
Examples: Simplify each expression
Get a common denominator - this is going to be our index
Rewrite as a radical

10. Remember we add exponents
Examples: Simplify each expression
Remember we add exponents

11. To rationalize the denominator we want an integer exponent
Examples: Simplify each expression
To rationalize the denominator we want an integer exponent

12. To rationalize the denominator we want an integer exponent
Examples: Simplify each expression
To rationalize the denominator we want an integer exponent

13. Examples: Simplify each expression

14. Examples: Simplify each expression

15. Multiply by conjugate and use FOIL
Examples: Simplify each expression
Multiply by conjugate and use FOIL

16. Examples: Simplify each expression

17. Examples: Simplify each expression

18. Examples: Simplify each expression

19. Examples: Simplify each expression