1. 4 minutes
Warm-Up
Simplify 1) 2) 3) 4)

2. 5.1 Exponents Objectives: To multiply numbers in exponential form
To divide numbers in exponential form
To simplify expressions with negative exponents

3. Multiplying Powers with Like Bases
For any rational number a, and for all whole numbers m and n,

4. Example 1
Simplify. Express using exponents. a) b) c) d)

5. Practice
Simplify. Express using exponents. a) b) c) d)

6. Dividing Powers with Like Bases
For any rational number a except 0, and for all whole numbers m and n,

7. Example 2
Simplify. Express using exponents. a) b) c)

8. Practice
Simplify. Express using exponents. a) b) c)

9. Negative Exponents
For any rational number a except 0, and for all whole numbers m and n,

10. Example 3
Express using positive exponents. a) b) c) d)

11. Practice
Express using exponents. 1) 2) 3)

12. The Exponent Zero
a0 = 1 for any rational number a except 0.

13. Example 4
Simplify. a) b) c) d)

14. Practice
Simplify. 1) 2) 3)

15. Warm-Up 5 minutes Write without exponents. 1) 2) 3)
Simplify. Express using exponents. 4) 5)

16. More with Exponents Objectives: To find a power of a power
To find a power of a product or quotient

17. Raising a Power to a Power
For any rational number a, and any whole numbers m and n,

18. Example 1 Simplify. Express using exponents. (52)3 = 56 (45)6 = 430

19. Practice Simplify. Express using exponents. 1) (54)3 2) (22)5 3) (a6)3
1) (54)3
2) (22)5
3) (a6)3
4) (n4)4

20. Example 2 Simplify. (5x)3 = (5x)(5x)(5x) = 125x3 (3z)2 = (3z)(3z)
= (2y2)(2y2)(2y2)(2y2)
= 16y8

21. Practice
Simplify.
1) (3y)2
2) (6m)4
3) (2a3)3
4) (4x3)2

22. Example 3 Simplify. (4x5y2)3 = 43x15y6 = 64x15y6 (-2x5y2)7 = -27x35y14
= (2y2)(2y2)(2y2)(2y2)
= 16y8

23. Practice
Simplify.
1) (4y3)4
2) (3x4y7z6)5
3) (-7x9y6)2

24. Example 4
Simplify.

25. 5 minutes
Warm-Up
Simplify
1) (34)3
2) (6x)3
3) (3x5)4
4) (-3m4n2)2 5)

26. Multiplying and Dividing Monomials
Objectives:
To multiply and divide monomials

27. Example 1 Multiply. (7y)(2y) = (7)(2)(y)(y) = 14y2 (5a3)(3a2)
(-3x3)(4xy5)
= (-3)(4)(x3)(x)(y5)
= -12x4y5

28. Practice
Multiply.
1) (3x)(-5)
2) (-m)(m)
3) (-x)2x3
4) (3p5q2)(4p2q3)

29. Practice Multiply. 5) (4x5y5)(-2x6y4) 6) (-7y4)(-y)(2y3)
7) (7a5)(3a3)(-a5)
8) (9b2)(2b5)(-3b7)

30. Example 2
Divide. 3 a 5 = 4 3 b 2 = a 2

31. Practice
Divide. 1) 2) 3) 4)