1. Rational Exponents Section 6.1
In other words, exponents that are fractions.

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

4. Examples:

5. Examples:

6. 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

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

8. Examples:

9. Approximating a Root with a Calculator
Use a graphing calculator to approximate:
SOLUTION: First rewrite as Then enter the following:
To solve simple equations involving xn, isolate the power and then take the nth root of each side.

10. Solving Equations Using nth Roots
A. 2x4 = 162
B. (x – 2)3 = 10

11. 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

12. 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

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

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

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

16. Examples: Simplify each expression

17. Examples: Simplify each expression

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

19. Examples: Simplify each expression

20. Examples: Simplify each expression

21. Examples: Simplify each expression

22. Examples: Simplify each expression