1. Rational Exponents
Fraction Exponents

2. Radical expression and Exponents
By definition of Radical Expression.
The index of the Radical is 3.

3. How would we simplify this expression?
What does the fraction exponent do to the number?
The number can be written as a Radical expression, with an index of the denominator.

4. The Rule for Rational Exponents

5. Write in Radical form

6. Write in Radical form

7. Write each Radical using Rational Exponents

8. Write each Radical using Rational Exponents

9. What about Negative exponents
Negative exponents make inverses.

10. What if the numerator is not 1 Always remember:
Evaluate

11. What if the numerator is not 1
Evaluate

12. What if the numerator is not 1
Evaluate

13. For any nonzero real number b, and integer m and n
Make sure the Radical express is real, no b<0 when n is even.

14. Simplify each expression
No fraction in the denominators.

15. Simplify each expression
No fraction in the denominators.

16. Simplify

17. Simplify

18. Simplify

19. Simplify in simplest radical form

20. Radical form:
Do # 68

21. Simplifying exponential expressions
If in radical form, transform to exponential form
Simplify by applying the exponent to each base.
Express with positive exponents or radical form, depending on the directions

22. Express in simplest form
Make exponential first!

23. Express in simplest form
Make exponential first!
Now simplify

24. Express in simplest form
Make exponential first!
Now simplify

25. Next example
Use positive exponents only!

26. Next example
Use positive exponents only!
Or in radical form:

27. Simplify

28. Simplify

29. Simplify

30. Simplify