lesson 15 - amazon s3...practice lesson 15 numerical expressions with exponents 166 lesson 15...

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Practice Lesson 15 Num

erical Expressions with Exponents

Unit 3

Practice and Prob

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Key

B Basic M Medium C Challenge

©Curriculum Associates, LLC Copying is not permitted. 161Lesson 15 Numerical Expressions with Exponents

Lesson 15

Name: Numerical Expressions with Exponents

Vocabularypower of ten a number

that can be written as a

product of tens

100 and 102 are powers

of ten

exponent the number

in a power that shows

how many times to

multiply the base by

itself

In the expression 102, the

exponent is 2 and the

base is 10

Prerequisite: Multiplying by a Power of 10

Study the example showing how to multiply by a power of 10. Then solve problems 1–7.

1 By how many factors of 10 did you multiply 0 008? Why?

2 Consider the expression 103 3 0 006

a. What is the exponent in the power of 10?

b. How many factors of 10 are in 103?

c. How do your answers to the last two questions relate to one another?

d. What is the value of 103 3 0 006?

Example

Find 102 3 0 008

Break 102 into a product of 10s and multiply

102 3 0 008 5 100 3 0 008 5 10 3 10 3 0.008

5 10 3 0.08

5 0 8

This means that 102 3 0 008 5 0 8

161161

I multiplied 0.008 by two factors of 10 because

102 5 100 5 10 3 10.

3

3

6

Possible answer: They are the same because

the exponent tells you how many times to

multiply 10 by itself.

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©Curriculum Associates, LLC Copying is not permitted.162 Lesson 15 Numerical Expressions with Exponents

Solve.

3 Complete the equations showing powers of 10 using exponents

a. 3 3 1,000 5 3 3 5

b. 0 07 3 100 5 0 07 3 5

c. 0 009 3 5 0 009 3 102 5

4 Find each product Explain how the place value of the digit 6 changes as the exponent changes

a. What is 0 006 3 101?

b. What is 0 006 3 102?

c. What is 0 006 3 103?

5 Describe the similarities and diff erences between 0 008 3 100 and 0 008 3 102

6 What power of 10 can you multipy 0 02 by to get a product of 20? Explain your answer

7 What is the product 4 3 1,000? Explain how you know

162

103

102

3,000

0.9

7

100

0.06

0.6

6

Possible answer: Similarities: Both expressions have a value of 0.8; both expressions

represent 0.008 multiplied by the same power of 10. Difference: The power of 10 is in

standard form in the first expression and is shown with an exponent in the second.

1,000 or 103; Possible explanation: I can multiply 0.02 by 10 to get 0.2, then by 10 again

to get 2, and by one more factor of 10 to get 20. So that is a total of three factors of 10,

or 1,000.

4,000; Possible explanation: There are three factors of 10 in 1000, so you multiply 4 by

10 three times to get 4,000.

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Possible explanation: As the exponent increases by 1, the place value of 6 is

10 times as great.

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Practice and Prob

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Unit 3




Name: Lesson 15

Write and Evaluate Expressions with Exponents

Study the example problem showing how to write and evaluate expressions with exponents. Then solve problems 1–9.

1 What does it mean to say that the amount of money from the previous month is quadrupled?

2 Represent the problem with repeated multiplication

Month Amount Saved (in dollars)

1 4

2 4 • 5 16

3

4

3 Write an expression using an exponent to represent the amount of money Adrian will have saved by month 4

4 What is the value of the expression you wrote in problem 3?

Example

Adrian wants to buy a skateboard that costs $85 After 1 month, he has $4 in savings and plans to quadruple the amount he has saved each month for 4 months Will Adrian have enough money to buy the skateboard in 4 months?

Month 1 Month 2 Month 3 Month 4

4 4 • 4 5 16 16 • 4 5 64 64 • 4 5 256

Adrian will have enough money to buy the skateboard in 4 months He will have $171 more than he needs

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When you quadruple an amount, you multiply by 4.

44

256

4

4 • 4 • 4 5 64

4 • 4 • 4 • 4 5 256

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Solve.

Use the following situation to solve problems 5–7.

Five students received the same text message at 9:00 AM. Each of them sent the message to 5 more students at 10:00 AM. Each of those students sent the message to 5 more students at 11:00 AM.

5 Represent the situation with exponential expressions Simplify the expressions

Time That Message Is Received

Number of Students ReceivingText Message

9:00 AM 51 5 5

10:00 AM

11:00 AM

6 If the pattern continues, how many students will receive the text message at noon? Explain how to use the pattern to fi nd the answer

7 If the pattern continues, at what time will 15,625 students receive the text message? Explain how you know

8 Write and simplify an expression to represent 63

9 Chin says that the value of 25 is 10 Explain what Chin did wrong and fi nd the correct value

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52 5 25

53 5 125

625 students; Possible explanation: The number of students who receive the text

message is multiplied by 5 each hour. So the number of students who will receive

the text message at noon is 54, which equals 625.

2:00 PM; Possible explanation: 54, or 625, students receive the message at noon. So at

1:00 PM, 55, or 3,125, students will receive the message. That means that at 2:00 PM, 56,

or 15,625, students will receive the message.

6 • 6 • 6 5 216

Chin multiplied 2 • 5 rather than multiplying 2 • 2 • 2 • 2 • 2; the value is 32.

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Solving

Unit 3 Exp

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Solve.

5 What is the value of 4 1 23 • 3?

Show your work.

Solution:

6 What is the value of 42 ·· 2 ? Describe the steps you took

to fi nd your answer

7 Darren and Barb each tried to evaluate 62 1 4 4 2

Darren Barb

62 1 4 4 2 62 1 4 4 2 5 36 1 4 4 2 5 36 1 4 4 2 5 40 4 2 5 36 1 2 5 20 5 38

Who evaluated the expression correctly? Explain what the other student did wrong

8 Use the numbers 8, 6, and 2 and one operation to write an expression that includes an exponent and has a value of 8 Use each number only once

9 Show where to place parentheses in the expression 4 1 32 • 5 2 2 so that the value of the expression is 31

4 1 32 • 5 2 2

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8; Find the value of 42 first because the order of operations tells you to evaluate

exponential expressions before you divide. Then divide 16 by 2.

Barb; Darren added 36 1 4 in the second step, but the order of operations tells

you to divide before adding. So he should have divided 4 by 2 before adding 36.

The value of 4 1 23 • 3 is 28.

4 1 23 • 3 5 4 1 8 • 35 4 1 245 28

26 4 8

( )

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Name: Lesson 15

Evaluate Expressions with Exponents

Study the example problem showing how to evaluate expressions with exponents. Then solve problems 1–9.

1 Explain why you must simplify 32 fi rst

2 Diallo says that the value of 12 2 32 is 81 How did he get that answer?

3 Maggie says that if the expression was 12 4 32, you would divide before simplifying 32 Is she right? Explain

4 Suppose the expression was (12 2 3)2 Would you still simplify 32 fi rst? Explain

Example

Follow the order of operations to simplify 12 2 32

First find 32 32 5 3 • 3 5 9

Then subtract 9 from 12 12 2 9 5 3

This means that:

12 2 32 5 12 2 9 5 3

The value of the expression is 3

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Possible answer: The order of operations says that you must simplify exponential

expressions before subtracting.

Possible answer: He did not follow the order of operations. He worked from left to

right. He subtracted 3 from 12 to get 9 and then found 92.

No; Using the order of operations, you simplify exponential expressions before

adding, subtracting, multiplying, or dividing.

No; Using the order of operations, you simplify expressions inside parentheses first.

B

B

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d Problem

Solving

Unit 3 Exp

ressions and Eq

uations

Unit 3




6 Students are getting signatures for a petition to increase sports activities at the community center The number of signatures they get each day is 3 times as many as the day before The expression 36 represents the number of signatures they got on the sixth day How many signatures did they get on the fi rst day?

A 3

B 6

C 18

D 729

Betsy chose B as the correct answer How did she get that answer?

Solve.

4 Which expression shows the fi rst step in evaluating

2 1 7 • 12 ·· 6 2 32?

A 2 1 84 ·· 6 2 32

B 9 • 12 ·· 6 2 32

C 2 1 7 • 12 ·· 6 2 9

D 2 1 7 • 2 2 32

5 Students at a cooking school made a supersized rectangular pizza for a class party Lupita cut the pizza into 3 equal pieces Then she cut each piece into 3 equal parts two more times Lupita needs 27 pieces of pizza Does she have enough pieces yet? Explain how you know

What do the base and the exponent represent?

What operation is done first in the order of operations?

How can you use exponents to help you solve this problem?

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Yes; 33 5 3 3 3 3 3 5 27. So Lupita has 27 pieces.

She confused the base with the exponent in 36.

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Name: Lesson 15

Numerical Expressions with Exponents

Solve the problems.

3 Beth is making a beanbag seat in the shape of a cube Each side of the seat is 2 feet long Beth needs to fi nd the volume of the seat so that she can buy the correct amount of beans Beans are sold in bags that hold 2 cubic feet of beans How many bags of beans should Beth buy?

Show your work.

Solution:

2 Look at the expression

4 • (12 2 8) 1 23

Tell whether each statement about the expression is True or False.

a. The last step in evaluating the expression is to simplify 23 u True u False

b. The value of 23 is 6 u True u False

c. The first step in evaluating the expression is to subtract 12 2 8 u True u False

d. The value of the expression is 48 u True u False

1 What is the value of 0 9 • 102?

A 0 09

B 0 9

C 9

D 90

What does the order of operations tell you?

How many factors of 10 are in 102?

How do you find the volume of a cube?

167

33

33

Possible student work: V 5 lwh V 5 2 ft • 2 ft • 2 ft; V 5 8 ft3

8 ft3 4 2 ft3 5 4

Beth should buy 4 bags of beans.

B

C

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lesson 15 - amazon s3...practice lesson 15 numerical expressions with exponents 166 lesson 15...

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