1. Index Laws Whenever we have variables which contain exponents and have equal bases, we can do certain mathematical operations to them. Those operations are called the “Index Laws” b x b = basex = exponent

2. Index Laws

3. Other Properties of Exponents Any single number or variable is always to the first power

4. Basic Examples

6. More Examples

8. nth Roots An nth root of number a is a number whose nth power is a. a number whose nth power is a If the index n is even, then the number a must be nonnegative. is not a real number

9. Square Root of x 2 Page 393

10. When n Is Even

11. Exponent 1/n When n Is Odd

12. Rational Exponents

13. Evaluating in Either Order

14. Negative Rational Exponents

15. Evaluating a -m/n

16. Rules for Rational Exponents 7-6

17. Simplifying

18. Simplifying

19. Simplifying

20. Multiplying Radicals – Different Indices

21. Different Indices

22. Rational Exponents Eliminate the root, then the power

23. Eliminate the Root, Then the Power

24. Negative Exponents

25. Eliminate the root, then the power

26. Negative Exponents Eliminate the root, then the power

27. Using the index templates on your CAS calculator:

28. No Solution Eliminate the root, then the power