1. Warm Up Find the product. 1. 5 • 5 • 5 • 5 625 2. 3 • 3 • 3 27
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Warm Up
Find the product.
Remember to subtract a negative number you add the opposite.
5. -5 – (-15)
6. 6 – (-10)
1. 5 • 5 • 5 • 5
625
2. 3 • 3 • 3 27 10 16
3. (–7) • (–7) • (–7)‏
–343
4. 9 • 9 81
Problem of the Day
What two positive integers when multiplied together also equal the sum of the same two numbers?
2 and 2

2. Learn to evaluate expressions with exponents.
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Learn to evaluate expressions with exponents.

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Vocabulary
exponential form
exponent
base
power

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exponential form: When a number is represented with an exponent. 42, 25 power: The number produced by raising a base to an exponent. Both 27 and 33 represent the same power.
Exponent
Base 7 2

5. Expanded Form
Base
Number of factors
Power
Evaluate
3 • 3 3 2 32 9
2 • 2 • 2 • 2 4 24
6 • 6 • 6 6
4 • 4 • 4 • 4
7 • 7 • 7 • 7 x4 Ω 42 1 5 a

6. What is the value of any power that has 1 as its base? Explain.
Write Pair Share…. Identify the base and the exponent in the power 54. Explain how to evaluate 54.
What is the value of any power that has 1 as its base? Explain.
Write the number 1000 using an exponent. Write the number 10,000 using an exponent.
Complete the statements. For each expression, identify the base and the exponent. How do the parentheses make the first expression different from the second expression?
(4x)2 = (4x) • ____
4x2 = 4 • ____ • ____
base: ____
exponent: _____
exponent: ______

7. Write in exponential form.
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Write in exponential form.
A. 4 • 4 • 4 • 4
Identify how many times 4 is a factor. 44
B. (–6) • (–6) • (–6)‏
Identify how many times –6 is a factor.
(–6)3
Read –(63) as “ negative 6 to the 3rd power” or “negative 6 cubed”.
Reading Math

8. Write in exponential form.
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Write in exponential form.
Identify how many times 5 and d are used as a factor.
C. 5 • 5 • d • d • d • d
52d4

9. Write in exponential form.
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Check It Out: Example 1
Write in exponential form.
A. x • x • x • x • x
Identify how many times x is a factor. x5
B. d • d • d
Identify how many times d is a factor. d3

10. Write in exponential form.
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Check It Out: Example 1
Write in exponential form.
C. 7 • 7 • b • b
Identify how many times 7 and b are used as a factor.
7 • 7 • b • b = 72b2

11. Additional Example 2: Simplifying Powers
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Additional Example 2: Simplifying Powers
Simplify.
A. 35
Find the product of five 3’s.
35 = 3 • 3 •
3 • 3 • 3
= 243
B. (-3)5
Find the product of five –3’s.
= (–3) • (–3) • (–3) • (–3) • (–3)‏
(–3)5
= –243
Helpful Hint
Always use parentheses to raise a negative number to a power.

12. Additional Example 2: Simplifying Powers
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Additional Example 2: Simplifying Powers
Simplify.
C. (–4)4
Find the product of four –4’s.
= (–4) • (–4) • (–4) • (–4)‏
(–4)4
= 256 D.
Find the product of eight 1/2’s.

13. Simplify. A. 74 Find the product of four 7’s. 74 = 7 • 7 • 7 • 7
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Check It Out: Example 2
Simplify.
A. 74
Find the product of four 7’s.
74 = 7 • 7 • 7 • 7
= 2401
B. (–9)3
Find the product of three –9’s.
= (–9) • (–9) • (–9)‏
(–9)3
= –729

14. Simplify. C. –(5)2 = –(5) • (5)‏ –(5)2 = –25 D. 97
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Check It Out: Example 2
Simplify.
C. –(5)2
Find the product of two 5’s and then make the answer negative.
= –(5) • (5)‏
–(5)2
= –25
D. 97
Find the product of seven 9’s.
97 = 9 • 9 • 9 • 9 • 9 • 9 • 9
= 4,782,969

15. Additional Example 3: Using the Order of Operations
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Additional Example 3: Using the Order of Operations
Evaluate x(yx – zy) + x for x = 4, y = 2, and z = 3. y
x(yx – zy) + xy
Substitute 4 for x, 2 for y, and 3 for z.
4(24 – 32) + 42
4(16 – 9) + 16
Evaluate the exponent.
4(7) + 16
Subtract inside the parentheses.
Multiply from left to right. 44
Add.

16. Evaluate z – 7(2x – xy) for x = 5, y = 2, and z = 60.
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Check It Out: Example 3
Evaluate z – 7(2x – xy) for x = 5, y = 2, and z = 60.
z – 7(2x – xy)
Substitute 5 for x, 2 for y, and 60 for z.
60 – 7(25 – 52)‏
60 – 7(32 – 25)
Evaluate the exponent.
60 – 7(7)
Subtract inside the parentheses.
60 – 49
Multiply from left to right. 11
Subtract.

17. Additional Example 4: Geometry Application
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Additional Example 4: Geometry Application
1 2
Use the expression (n2 – 3n) to find the number of diagonals in a 7-sided figure.
(n2 – 3n)‏ 1 2
(72 – 3 • 7)‏ 1 2
Substitute the number of sides for n.
(49 – 3 • 7)‏ 1 2
Evaluate the exponent.
(49 – 21)‏ 1 2
Multiply inside the parentheses.
(28)‏ 1 2
Subtract inside the parentheses.
14 diagonals
Multiply

18. Additional Example 4 Continued
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Additional Example 4 Continued
A 7-sided figure has 14 diagonals. You can verify your answer by sketching the diagonals.

19. (n2 – 3n)‏ (42 – 3 • 4)‏ (16 – 3 • 4)‏ (16 – 12)‏ (4)‏ 2 diagonals
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Check It Out: Example 4
1 2
Use the formula (n2 – 3n) to find the number of diagonals in a 4-sided figure.
(n2 – 3n)‏ 1 2
(42 – 3 • 4)‏ 1 2
Substitute the number of sides for n.
(16 – 3 • 4)‏ 1 2
Evaluate the exponents.
(16 – 12)‏ 1 2
Multiply inside the parentheses.
(4)‏ 1 2
Subtract inside the parentheses.
2 diagonals
Multiply.

20. Check It Out: Example 4 Continued
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Check It Out: Example 4 Continued
A 4-sided figure has 2 diagonals. You can verify your answer by sketching the diagonals.

21. Lesson Quiz for Student Response Systems
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Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems 21

22. Write in exponential form.
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Lesson Quiz: Part I
Write in exponential form.
1. n• n • n• n 4 n
2. (–8) • (–8) • (–8) • (h)
(–8)3h
3. Evaluate (–4)4
256
4. Evaluate x • z – yx for x = 5, y = 3, and z = 6.
–213

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Lesson Quiz: Part II
5. A population of bacteria doubles in size every minute. The number of bacteria after 5 minutes is 15  25. How many are there after 5 minutes?
480

24. Lesson Quiz for Student Response Systems
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Lesson Quiz for Student Response Systems
1. Write g• g • g• g• g in exponential form.
A. 5g
B. g + 5
C. g5
D. g5 24

25. Lesson Quiz for Student Response Systems
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Lesson Quiz for Student Response Systems
2. Evaluate (–3)4.
A. 12
B. –12
C. 81
D. –81 25

26. Lesson Quiz for Student Response Systems
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Lesson Quiz for Student Response Systems
3. Evaluate gh + 3k – gk for g = 2, h = 4, and k = 3.
A. 6
B. 7
C. 9
D. 11 26