Rational Exponents

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

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

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

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

6. When a base is raised to a rational exponent of the form m/n we use the following definition: The numeratorm becomes the … exponent. The denominatorn becomes the … index. The baseb becomes the … radicand.

7. or • Example 3 Write the following using radical notation. Simplify the radical if possible:

8. or • Example 4 Whenever the radical can be simplifiedeasily, the second form is the one to use.

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

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

11. 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. Example 6 Write the following using positive exponents. Simplify if possible:

13. Example 7

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

15. Example 8

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