This document provides examples for simplifying exponential expressions according to the laws of exponents. It contains 24 examples divided into 4 categories: (1) expressions of the form a^b, (2) expressions of the form a^b/c, (3) expressions of the form a^b/c^d, and (4) expressions of the form a^b/c^d, with the examples exploring different sign combinations for the exponents a, b, c, and d. The goal is to demonstrate how to simplify various exponential expressions using the laws of exponents.

1. The Laws of Exponents

2. Overview
This set of tutorials provides 24 examples of the laws of
exponents. They fall into four categories:
1.Simplifying exponential expressions of the form
(Examples 1-4).
2.Simplifying exponential expressions of the form
(Examples 5-12).
3.Simplifying exponential expressions of the form
(Examples 13-16).
4.Simplifying exponential expressions of the form
(Examples 17-24).

3. Example 1: Simplifying exponential expressions of the form
, where a > 0, b > 0.

4. Example 2: Simplifying exponential expressions of the form
, where a < 0, b > 0.

5. Example 3: Simplifying exponential expressions of the form
, where a > 0, b < 0.

6. Example 4: Simplifying exponential expressions of the form
, where a < 0, b < 0.

7. Example 5: Simplifying exponential expressions of the form
, where a > 0, b > 0, c > 0.

8. Example 6: Simplifying exponential expressions of the form
, where a < 0, b > 0, c > 0.

9. Example 7: Simplifying exponential expressions of the form
, where a > 0, b < 0, c > 0.

10. Example 8: Simplifying exponential expressions of the form
, where a > 0, b > 0, c < 0.

11. Example 9: Simplifying exponential expressions of the form
, where a < 0, b < 0, c > 0.

12. Example 10: Simplifying exponential expressions of the form
, where a > 0, b < 0, c < 0.

13. Example 11: Simplifying exponential expressions of the form
, where a < 0, b > 0, c < 0.

14. Example 12: Simplifying exponential expressions of the form
, where a < 0, b < 0, c < 0.

15. Example 13: Simplifying exponential expressions of the form
, where a > 0, b > 0.

16. Example 14: Simplifying exponential expressions of the form
, where a < 0, b > 0.

17. Example 15: Simplifying exponential expressions of the form
, where a > 0, b < 0.

18. Example 16: Simplifying exponential expressions of the form
where a < 0, b < 0.

19. Example 17: Simplifying exponential expressions of the form
, where a > 0, b > 0, c > 0.

20. Example 18: Simplifying exponential expressions of the form
, where a < 0, b > 0, c > 0.

21. Example 19: Simplifying exponential expressions of the form
, where a > 0, b < 0, c > 0.

22. Example 20: Simplifying exponential expressions of the form
, where a > 0, b > 0, c < 0.

23. Example 21: Simplifying exponential expressions of the form
, where a < 0, b < 0, c > 0.

24. Example 22: Simplifying exponential expressions of the form
, where a > 0, b < 0, c < 0.

25. Example 23: Simplifying exponential expressions of the form
, where a < 0, b > 0, c < 0.

26. Example 24: Simplifying exponential expressions of the form
, where a < 0, b < 0, c < 0.