Working with Powers

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

2. 2 × 2 = • 2 × 2 × 2 = • 2 × 2 × 2 × 2 = • How can we write these in shorter notation?

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

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

5. Integer Exponents • Base 4 • Exponent 3 • 43 is called a power • 43 = 4 x 4 x 4 • = 64

6. You try these . . . • 72 • 54 • 210

7. Operations with Exponents • Multiply (x3)∙(x4) = (x ∙ x ∙ x) ∙ (x ∙ x ∙ x ∙ x) = (x ∙ x ∙ x ∙ x ∙ x ∙ x ∙ x) = x7 A5∙ A4 = • Divide:

8. Exponent Rules #1 n times

9. Zero as an exponent • 40 • 90 • 170

10. Exponent Rules #2

11. a0 = 1 • M0 • (pq)0 • (2x2y)0

12. 3-1 7-1 5-2 2-4 (1/2) -1 (3/4) -2 Negative Exponents

13. Exponent Rules #3

14. M-2 • x-5 • (1/y)-3

15. Combining Exponents aman=?

16. Exponent Rules #4

17. y-2y7 m6m-6 2z-3z5w-6w-2 • x5x4 • b3b-6 • (2x3)(4x-2)

18. Combining Exponents am/an=?

19. Exponent Rules #5

21. Combining Exponents (am)n=?

22. Exponent Rules #6

23. (w4)5 • (p-3)4 • (5x4)-2 • (-3y-7)3

24. Combining Exponents

25. Exponent Rules #7 (distributive rule for exponents)

27. Exponent Rules • 1. • 2. • 3.

28. 4. 5. 6. 7. Exponent Rules