1. B11 Exponents and Scientific Notation

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

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

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

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

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

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

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

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

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

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

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

13. Practice
Simplify. 1) 2) 3)

14. Practice Write without exponents. 1) 2) 3)
Simplify. Express using exponents. 4) 5)

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

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

17. 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

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

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

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

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

22. Example 4
Simplify.

23. Practice
Simplify
1) (34)3
2) (6x)3
3) (3x5)4
4) (-3m4n2)2 5)

24. Multiplying and Dividing Monomials

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

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

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

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

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