1. Table of Contents Rational Exponents When a base is raised to a rational exponent of the form 1/n we use the following definition: The denominator of the rational exponent … … becomes the index of the radical... …and the base of the exponential … … becomes the radicand of the radical.

2. Table of Contents Example 1 Write each of the following using radical notation. Simplify the radical if possible:

3. Table of Contents Example 2 Write each of the following in rational exponent form:

4. Table of Contents When a base is raised to a rational exponent of the form m/n we use the following definition: The numerator m becomes the …exponent.

5. Table of Contents When a base is raised to a rational exponent of the form m/n we use the following definition: The numerator m becomes the …exponent. The denominator n becomes the …index.

6. Table of Contents When a base is raised to a rational exponent of the form m/n we use the following definition: The numerator m becomes the …exponent. The denominator n becomes the …index. The base b becomes the …radicand.

7. Table of Contents Example 3 Write the following using radical notation. Simplify the radical if possible: or

8. Table of Contents or Whenever the radical can be simplified easily, the second form is the one to use. Example 4

9. Table of Contents Example 5 Write the following in rational exponent form:

10. Table of Contents When a base is raised to a negative rational exponent we use the following definition:

11. Table of Contents When a rational base is raised to a negative rational exponent we use the following: Take the reciprocal of the rational expression and make the exponent positive.

12. Table of Contents Example 6 Write the following using positive exponents. Simplify if possible:

13. Table of Contents Example 7

14. Table of Contents Example 8 Take the reciprocal of the rational expression and make the exponent positive.

15. Table of Contents Example 8

16. Table of Contents