1. Power2525 2424 23232 2121 2020 2 -1 2 -2 2 -3 2 -4 2 -5 Value Zero and Negative Exponents

2. _________________________ Zero exponent: Examples:

3. _______________________ Negative exponent: Think: Examples:

5. Simplify. 4 -3 7 0 (-5) -4 -5 -4 One cup is 2 -4 gallons. What does this mean in simplified terms?

6. Try it! Simplify. 10 -4 (-2) -4 (-2) -5 -2 -5 A sand fly may have a wingspan up to 5 -3 m. What does this mean in simplified terms?

7. Multiplication of Exponents Recall: 4 3 (exponential notation) (expanded form) (simplified form)

8. Product of Powers 2 2 2 3 Expanded form: Exponential notation: What is the “rule”? We can multiply powers only when ________________!!

9. What happens when bases are not the same?? 2 3 3 2 We must ________________________________ Exponents _______________________________ ________________________________________

10. Examples: 5 3 ∙ 5 2 (-2)(-2) 4 *NO exponent implies a power of 1 x 2 ∙ x 3 ∙ x 4

11. BE CAREFUL… These are not the same!!! -2 2 (-2) 2 “The opposite of 2 2 ” -2 ∙ -2 or or -(2 2 ) (-2) (-2)

12. -3 3 (-3) 3 -3 2 (-3) 2

13. POWER OF A POWER (3 2 ) 3 3 2 ∙ 3 2 ∙ 3 2 (product of a power) 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 (expanded form)

14. Rather than writing out a problem in an expanded form, use the “shortcut” Rule: When given a power of a power, ______________ the exponents. (x a ) b = x a∙b

15. For example: (x 3 ) 4 (x 2 ) 5

16. Try these on your own… (3 3 ) 2 (p 4 ) 4 (n 4 ) 5 [(-3) 5 ] 2

17. POWER OF A PRODUCT (xy) 3 (x 2 y 3 z) 5 (4∙3) 2 (-3xy) 4 Rule: When given a power of a product, _________ _________________________________________

18. Try these on your own… (st) 2 (4yz) 3 (-2x 4 y 7 z 9 ) 5 (-x 2 y 8 ) 3

19. REVIEW Product of Powers (ADD the exponents) x a ∙x b = x a+b Power of a Power (MULTIPLY the exponents) (x a ) b = x a∙b Power of a Product (“DISTRIBUTE” the exponents) (xy) a = x a y a

20. Now put it all together! (3b) 3 b-4x (x 3 ) 2 2x 3 (-3x) 2 4x (-x x 3 ) 2 (abc 2 ) 3 ab(5y 2 ) 3 (y 3 ) 2

21. Division Properties of Exponents The Quotient of Powers To divide powers that have the same base, you _____________________________ Ex:

22. Simplify the following.

23. Power of a Quotient

24. Simplify the following.

25. Try It!

26. Using more than one property… a) b)

30. Give it a try:

31. Challenge:

32. Review Anything raised to a zero power is… When you have a negative exponent…

33. Try It!

34. Points to remember…

35. Warm Up