2. Main Idea and New Vocabulary Example 1: Write Expressions Using Powers
Example 6: Evaluate Powers
Example 7: Evaluate Powers
Example 8: Real-World Example
Key Concept: Order of Operations
Example 9: Evaluate Algebraic Expressions
Example 10: Evaluate Algebraic Expressions
Lesson Menu

3. Use powers and exponents to write large and small numbers.
base
exponent
Main Idea/Vocabulary

4. Write Expressions Using Powers
Write 7 • 7 • 7 • 7 using exponents.
The base 7 is a factor 4 times. So, the exponent is 4.
7 • 7 • 7 • 7 = 74
Answer: 74
Example 1

5. Write 11 • 11 • 11 • 11 • 11 • 11 using exponents.
A. 6 • 11
B. 611
C. 116
D. 117
Example 1 CYP

6. Write Expressions Using Powers
Write (–9)(–9)(–9) using exponents.
The base –9 is a factor 3 times. So, the exponent is 3.
(–9)( –9)(–9)= (–9)3
Answer: (–9)3
Example 2

7. Write (–4)(–4)(–4)(–4)(–4) using exponents.
A. (–4)4
B. (–4)5
C. (–4)(5)
D. 5–4
Example 2 CYP

8. Write Expressions Using Powers
Write a • a • a • a • a using exponents.
The base a is a factor 5 times. So, the exponent is 5.
a • a • a • a • a = a5
Answer: a5
Example 3

9. Write y • y • y • y • y • y • y using exponents.
A. y7
B. y6
C. 7y
D. 7y
Example 3 CYP

10. Write Expressions Using Powers
Write 4 • 4 • 6 • 6 • 6 • 6 • 6 using exponents.
4 • 4 • 6 • 6 • 6 • 6 • 6 = (4 • 4) • (6 • 6 • 6 • 6 • 6) Associative Property
= 42 • 65 Definition of exponents
Answer: 42 • 65
Example 4

11. Write (–2) • (–2) • (–2) • 7 • 7 using exponents.
A. (–2) • 7
B. (–2)3 • 73
C. (–2)3 • 72
D. (–2)(3) • 72
Example 4 CYP

12. Write Expressions Using Powers
Write x • y • x • y • x • x using exponents.
x • y • x • y • x • x = x • x • x • x • y • y Commutative Property
= (x • x • x • x) • (y • y) Associative Property
= x4 • y2 Definition of exponents
Answer: x4 • y2
Example 5

13. Write j • j • k • k • j using exponents.
A. j • k
B. 3j • 2k
C. j3 • k2
D. j2 • k3
Example 5 CYP

14. (–5)2 = (–5) • (–5) Write the power as a product. = 25 Multiply.
Evaluate Powers
Evaluate (–5)2.
(–5)2 = (–5) • (–5) Write the power as a product.
= 25 Multiply.
Answer: 25
Example 6

15. Evaluate (–4)5.
A. –1,024
B. –20
C. 625
D. 1,024
Example 6 CYP

16. Write the power as a product.
Evaluate Powers
Evaluate
Write the power as a product.
Multiply.
Answer:
Example 7

17. Evaluate A. B. C. D.
Example 7 CYP

18. 2 • 42 • 52 = 2 • 4 • 4 • 5 • 5 Write the power as a product.
RACQUETBALL A racquetball court has an area of 2 • 42 • 52 square feet. What is the area of the racquetball court?
2 • 42 • 52 = 2 • 4 • 4 • 5 • 5 Write the power as a product.
= 2 • (4 • 4) • (5 • 5) Associative Property
= 2 • 16 • 25 or 800 Multiply.
Answer: The racquetball court has an area of about square feet.
Example 8

19. GARDENS A community vegetable garden has an area of 3 • 43 • 62 square feet. What is the area of the garden?
A. 72 square feet
B. 1,152 square feet
C. 1,296 square feet
D. 6,912 square feet
Example 8 CYP

20. Key Concept 9

21. Evaluate Algebraic Expressions
Evaluate x3 + y5 if x = 4 and y = 2.
x3 + y5 = Replace x with 3 and y with 2.
= (4 • 4 • 4) + (2 • 2 • 2 • 2 • 2) Write the powers as products.
= or 96 Add.
Answer: 96
Example 9

22. Evaluate a4 – b2 if a = 3 and b = 5.
C. 4
D. 2
Example 9 CYP

23. Evaluate Algebraic Expressions
Evaluate (x + y)2 if x = 4 and y = 2.
(x + y)2 = (4 + 2)2 Replace x with 4 and y with 2.
= 62 Perform operations in the parentheses first.
= 6 • 6 or 36 Write the powers as products. Then simplify.
Answer: 36
Example 10

24. Evaluate (r + s)4 if r = –3 and s = 7.
B. 81
C. 256
D. 10,000
Example 10 CYP