1. Properties of Exponents
Examples and Practice

2. Product of Powers Property
How many factors of x are in the product x3∙x2?
Write the product as a single power.
In general:
5 factors: x∙x∙x∙x∙x
x∙x∙x∙x∙x = x5
xm∙xn= xm + n

3. Question #1
Simplify the expression:
a3a5
a. a15 b. a8
c. a2 d. 1/a2

4. Question #2 Simplify the expression: (3m2)(2m4) a. 6m8 b. 5m6
c. 5m8 d. 6m6

5. Question #3 Simplify the expression: (-2xy3)(5x4y2)
a. -10x5y5 b. -10x4y5
c. 3x5y5 d. -10x4y6

6. Power of a Power Property
How many factors of x are in the expression (x3)2?
Write the product as a single power.
In general:
6 factors: x∙x∙x∙x∙x∙x
(x∙x∙x)∙(x∙x∙x) = x6
(xm)n= xm∙n

7. Question #4
Simplify the expression:
(42)5
a b
c d. 167

8. Question #5
Simplify the expression:
(x3)4
a. x7 b. 2x7
c. x12 d. 2x12

9. Power of a Product Property
How many factors of x and y are in the expression (xy)2?
Simplify the expression.
In general:
2 factors of each: (x∙y)∙(x∙y)
(x∙y)∙(x∙y) = x2y2
(x∙y)m= xmym

10. Question #6 Simplify the expression: (b3c2)4 a. b7c6 b. b12c8
c. b7c8 d. 2b12c8

11. Question #7 Simplify the expression: (-3a3b)2 a. 6a5b2 b. 9a5b2
c. -9a6b2 d. 9a6b2

12. Question #8 Simplify the expression: (-3a3b)2(2ab) a. 36a7b3 b. 18a7b3
c. -6a7b3 d. -18a7b3

13. Quotient of Powers Property
Simplify the expression.
In general:

14. Question #9
Simplify the expression:
a. a5 b. a9
c. 1/a5 d. 1/a9

15. Question #10
Simplify the expression:
a. a5 b. 6
c. 1/a5 d. 1/6

16. Question #11 Simplify the expression: a. -3a5 b. -16a5
c. -3a8 d. -16a8

17. Question #12
Simplify the expression:
a. b.
c. d a4b3

18. Power of a Quotient Property
Simplify the expression.
In general:

19. Question #13
Simplify the expression:
a. b.
c. d

20. Question #14
Simplify the expression:
a. b.
c. d.

21. Negative Exponent Property
In general:

22. Question #15 Simplify the expression: (34)(3-2) a. 38 b. 3-8
c d. 32

23. Question #16
Simplify the expression:
a. b.
c. d.

24. Question #17
Simplify the expression:
a b. 26
c d.

25. Question #18
Simplify the expression:
a. b.
c. d.

26. Question #19
Simplify the expression:
a. b.
c. d.

27. Zero Exponent Property
In general:

28. Question #20
Simplify the expression: x0y-2
a. b. xy2
c. y2 d.