1. Tuesday June 17: Laws of Exponents

2. Definitions
Monomial: a number, variable, or the product of a number and one or more variables
Constant: number

3. 32 · 34
= 3 · 3 · 3 · 3 · 3 · 3
= 36

4. Product of Powers
To multiply two powers that have the same base, add the exponents.
Example: xa · xb = xa+b

5. Examples: Example 1: (5x6)(x3) = 5·x·x·x·x·x·x · x·x·x = 5x9
or 5x6+3 = 5x9
Example 2: (4ab3)(-7a2b2)
= 4·a·b·b·b · -7·a·a·b·b
= 4·-7·a·a·a·b·b·b·b·b
= -28a3b5
or -28a1+2b3+2 = -28a3b5

6. (k2)4
= k2·k2·k2·k2
= k
= k8

7. Power of a Power
When you have an exponent raised to another exponent, multiply the exponents.
Example: (am)n = km·n

8. (xy)4
= xy·xy·xy·xy
= x4y4

9. Power of a Product
When you have an product raised to an exponent, apply the exponent to each factor.
Example: (ab)m = ambm

10. Example: (-2a4b2)3
= (-2)3(a4)3(b2)3
= -8a12b6

11. Practice

12. NOTE!!!
(-2)3 = -8
(-2)4 = 16
-23 = -8
-24 = -16

13. Your turn!
p.173 #1-37 odd

14. Laws of Exponents Continued

15. Example: = =

16. Quotient of Powers
To divide two powers that have the same base, subtract the exponents.
Example: = =

17. Examples:
Example 1:
Example 2: = = = =

18. Practice

19. Your turn!
p.213 #1-29 odd

20. Negative Exponents

21. 51 5 50 1 1 = = 51 5
So any base to the power 0 equals 1.
Examples:

22. a-3 a3 a0 · = = 1 So that must mean… · a3
So a negative exponent means…flip it and change the exponent to positive

23. Examples = 1 1 = = 21 b3
2b3

24. Practice
Express without any negative exponents.

25. Your turn!
p.218 #1-7 odd, odd