1. Identify the exponent and the base in the expression 138.
Skills Check
Identify the exponent and the base in the
expression 138. 2.
x2 when x = 10 3. = 3
a3 when a 4. =
1.2
m2 when m

2. Standards: Objectives:
2.0 Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents.
Objectives:
Use the product of powers property
Use the power of a power property
Use the power of a product property
Use all three properties

3. What is the expanded form of 23

5. Example 1 a. • ( ) 2 5 – 2 3 = ( ) 2 3 5 – + ( ) – 2 8 = b. • x4 x3 =
Use the product of powers property a. • ( )
2 5 –
2 3 = ( ) – + ( ) –
2 8 = b. • x4 x3 =
x4 3 + = x7 c. • 76 7 78 = • 71 78 76 = 7 + =
715

6. Example 1 d. • y y3 y2 = • y3 y2 y1 = 1 3 2 y + = y6
Use the product of powers property d. • y y3 y2 = • y3 y2 y1 = y + = y6

7. Simplify the expression.
Guided Practice
for Example 1
Simplify the expression. 1. 32 • 37 2. ( ) 5 – •
5 9 3. • z5 4. • x6 x x2

8. Multiple Choice Practice
Example 2
Multiple Choice Practice
Which expression is equivalent to w3w2?
w3w3
w4w
w5w
w9w4
SOLUTION
STEP 1 Simplify the given expression, w3w2.
w3w2 w = + w5
STEP 2 Determine which expression equals . 5 w
w3w3 = +
Choice A: w6

9. Multiple Choice Practice
Example 2
Multiple Choice Practice
Choice B:
w4w =
w4w1 = w = w5 +
ANSWER
The correct answer is B. 9

11. [ ] Use the power of a power property Example 3 a. ( ) 2 3 5 = 25 3 • • =
215 = ( ) 6 – • b. ( ) [ ] 2 6 – 5 = ( ) 6 – 10 c. ( ) x 4 2 = x • = x8 11

12. [ ] Use the power of a power property Example 3 = ( ) 2 + y 6 2 • d. ( • d. ( ) [ ] 6 2 + y = 12 ( ) 2 + y 12

13. [ ] for Examples 2 and 3 Guided Practice Simplify the expression. 5. m• m 8 9 6. ( ) 4 2 7. ( ) [ ] 4 2 – 5 8. ( ) x 7 5

15. Example 4 a. ( ) 24 13 • 8 = 248 138 • b. ( 9xy ) 2 81x2y2 = ( 9 ) 2 •
Use the power of a product property a. ( ) 24 13 • 8 =
248
138 • b. (
9xy ) 2
81x2y2 = ( 9 ) 2 • x y 92 x2 y2 c. ( 4z ) 2 – =
16z2 ( 4 ) 2 • – z z2 ( 4z ) 2 – d. = 42 • z2 – ( )
16z2
4 z 2

16. Example 5 Simplify ( ) 2x 2 x4. 3 • ( ) 2x3 2 = x4 22 • x 3 = 4 • x6
Use all three properties
Simplify ( ) 2x 2
x4. 3 • ( )
2x3 2 = x4 22 • x 3
Power of a product property = 4 • x6 x4
Power of a power property =
4x10
Product of powers property

17. Simplify the expression.
Guided Practice
for Examples 4 and 5
Simplify the expression. 9. ( ) 42 12 • 2
10. ( ) 3n – 2
11. (
9m n ) 4 3
12. ( 5x ) 4 2 5 •

18. In 2003 the U.S. Department of Agriculture (USDA)
Example 6
Solve a real-world problem
BEES
In 2003 the U.S. Department of Agriculture (USDA)
collected data on about 103 honeybee colonies. There
are about 104 bees in an average colony during honey
production season. About how many bees were in the
USDA study?
SOLUTION
To find the total number of bees, find the product
of the number of colonies, 103, and the number of
bees per colony, 104. •
103
104 10 = +
107 18

19. The USDA studied about 107 , or 10,000,000 bees.
Example 6
Solve a real-world problem
ANSWER
The USDA studied about 107 , or 10,000,000 bees.

20. Guided Practice
for Example 6
13.
WHAT IF? In Example 6, about 102 honeybee colonies in the study were located in Idaho. About how many bees were studied in Idaho?

21. Evaluate the expression.
Skills Check
Evaluate the expression.
r2 when r 7. = 6 5
z3 when z 8. = 2 1
Evaluate the expression. 9. 81
10. 64 –

22. Evaluate the expression.
Skills Check
Evaluate the expression.
100
11. – + –
12.
121
Use the distributive property to write an equivalent expression.
13. ( ) 3 – y 4
14. ( ) 2 – x

23. Use the distributive property to write an equivalent expression.
Skills Check
Use the distributive property to write an equivalent expression.
15. – x ( x + 11 )
16. ( ) 9 – x 4x

24. Standards: Objectives:
2.0 Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents.
Objectives:
Use the product of powers property
Use the power of a power property
Use the power of a product property
Use all three properties