1. Fall 20041 Working with Powers Integer Exponents Exponent Rules Order of Operations

2. Fall 20042 Examples 2 × 2 = 2 × 2 × 2 = 2 × 2 × 2 × 2 = How can we write these in shorter notation?

3. Fall 20043 Examples Multiplication is a shortcut for repeated addition. Exponents are a shortcut for repeated multiplication. 3 + 3 + 3 + 3 + 3 = 5 × 3 3 × 3 × 3 × 3 × 3 =

4. Fall 20044 Write these numbers using exponential notation: 10,000 = 10 ? 27 = 3 ? 32 = 2 ?

5. Fall 20045 Computer Memory A byte is capable of storing one letter of the alphabet. For example, the word “math” requires four bytes to store in a computer. Bytes of computer memory are often manufactured in amounts equal to powers of 2.

6. Fall 20046 For Example 1 kilobyte (1K) = 2 10 = 1 megabyte (1 MB) = 2 20 =

7. Fall 20047 Integer Exponents Base 4 Exponent 3 4 3 is called a power 4 3 = 4 x 4 x 4 = 64

8. Fall 20048 You try these... 7 2 5 4 2 10

9. Fall 20049 Operations with Exponents Multiply (x 3 )∙(x 4 ) = (x ∙ x ∙ x) ∙ (x ∙ x ∙ x ∙ x) = (x ∙ x ∙ x ∙ x ∙ x ∙ x ∙ x) = x 7 A 5 ∙ A 4 = Divide:

10. Fall 200410 Exponent Rules #1 n times

11. Fall 200411 Zero as an exponent 4 0 9 0 17 0

12. Fall 200412 Exponent Rules #2

13. Fall 200413 a 0 = 1 M 0 (pq) 0 (2x 2 y) 0

14. Fall 200414 Negative Exponents 3 -1 7 -1 5 -2 2 -4 (1/2) -1 (3/4) -2

15. Fall 200415 Exponent Rules #3

16. Fall 200416 M -2 x -5 (1/y) -3

17. Fall 200417 Combining Exponents a m a n =?

18. Fall 200418 Exponent Rules #4

19. Fall 200419 y -2 y 7 m 6 m -6 2z -3 z 5 w -6 w -2 x 5 x 4 b 3 b -6 (2x 3 )(4x -2 )

20. Fall 200420 Combining Exponents a m /a n =?

21. Fall 200421 Exponent Rules #5

22. Fall 200422

23. Fall 200423 Combining Exponents (a m ) n =?

24. Fall 200424 Exponent Rules #6

25. Fall 200425 (w 4 ) 5 (p -3 ) 4 (5x 4 ) -2 (-3y -7 ) 3

26. Fall 200426 Combining Exponents

27. Fall 200427 Exponent Rules #7 (distributive rule for exponents)

28. Fall 200428

29. Fall 200429 Exponent Rules 1. 2. 3.

30. Fall 200430 Exponent Rules 4. 5. 6. 7.