Points Differentiated Remediation

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5 Assess & RemediateAssign the Lesson Quiz. Appropriate intervention, practice, or enrichment is automatically generated based on student performance.

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Need toreview

0 2 4 6 8 10

Math Success

Lesson Check

=

= undefined

xn

a-nb0anxn

b0

anxn

0

197 Lesson 7-1

Check off the vocabulary words that you understand.

exponent zero exponent negative exponent

Rate how well you can simplify zero and negative exponents.

• Do you UNDERSTAND?

Error Analysis A student incorrectly simplifi ed xn

a2nb0 as

shown at the right. Find and correct the student’s error.

25. Did the student work correctly with —

base x? Yes / No base a? Yes / No base b? Yes / No

26. What error did the student make?

_____________________________

_____________________________

23. Now solve the problem.

24. What does each value represent?

For w 5 22, the value For w 5 0, the value For w 5 1, the valuerepresents the number represents the number represents the number of insects 9. of insects 9. of insects 9.

27. Now simplify the expression correctly.

Solutions may vary. Sample:

For w 522: For w 5 0: For w 5 1:

5400 ? 3w 5 5400 ? 322 5400 ? 3w 5 5400 ? 30 5400 ? 3w 5 5400 ? 31

5 5400 ? 19 5 5400 ? 1 5 5400 ? 3

5 600 5 5400 5 16,200

600 5400 16,200

2 weeks before the when the population 1 week after the

population was measured was measured population was measured

The student simplified b0 as

0 instead of as 1.

Solutions may vary. Sample:

xn

a2n b0 5xnan

b0 5 xnan1 5 xnan

HSM11A1MC_0701.indd 197 2/14/09 5:56:45 AM

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Vocabulary

Chapter 7 194

7-1 Zero and Negative Exponents

Review

Circle the exponent in each equation.

1. 35 5 243 2. 72 5 49 3. 27 5 128

Write an equivalent expression using an exponent.

4. 35 ? 35 ? 35 5 5. 19 ? 19 ? 19 ? 19 ? 19 ? 19 ? 19 ? 19 ? 19 5

6. In the expression 43, identify the base and the exponent.

base = exponent =

Vocabulary Builder

negative (adjective) NEG uh tiv

Definition: A negative quantity has a value less than zero.

Examples: 23,212, and 2p are all negative numbers.

Use Your Vocabulary

7. Write a number to represent each situation.

The temperature is 4 degrees You owe your brother A worker’s hourly pay below zero. eight dollars. increases by $.50.

Draw a line from each negative number in Column A to its opposite in Column B.

Column A Column B

8. 212 17

9. 2335 1

2

10. 217 335

The symbol for

is

negative

353 199

4

24

3

2$ 8 $.50

HSM11A1MC_0701.indd 194 2/20/09 12:23:27 PM

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Properties Zero and Negative Exponents

11. Complete the table.

Exponent Property Examples

ZeroFor every nonzeronumber a,

(a)0 1 ( 24)0 1

60 1

Negative

7 3 173

1343

4 2 142

1

16

( 3) 5 1( 3)5

1

243

For every nonzeronumber a and integer n,

1an(a) n

Write T for true or F for false.

12. 922 5

181

13. (29)0 5 21

14. 921 5 2

19

15. 923 5

127

Problem 1

Problem 2

195 Lesson 7-1

Simplifying Powers

Got It? What is the simplified form of 423?

16. Complete each step to simplify 423.

423 51

4

Move the power to the denominator and make the exponent positive.

51

Evaluate the power to simplify the expression.

Simplifying Exponential Expressions

Got It? What is the simplified form of each expression?

x29 1n23 4c23b 2

a23 n25

m2

Underline the correct word to complete each sentence.

17. To simplify a base in the numerator that has a negative exponent, move the base to the denominator and write a positive / negative exponent.

18. To simplify a base in the denominator that has a negative exponent, move the base to the numerator and write a positive / negative exponent.

T F F F

3

64

HSM11A1MC_0701.indd 195 2/14/09 5:56:36 AM

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c. o

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aff

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Res

erve

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Vocabulary

Chapter 7 194

7-1 Zero and Negative Exponents

Review

Circle the exponent in each equation.

1. 35 5 243 2. 72 5 49 3. 27 5 128

Write an equivalent expression using an exponent.

4. 35 ? 35 ? 35 5 5. 19 ? 19 ? 19 ? 19 ? 19 ? 19 ? 19 ? 19 ? 19 5

6. In the expression 43, identify the base and the exponent.

base = exponent =

Vocabulary Builder

negative (adjective) NEG uh tiv

Definition: A negative quantity has a value less than zero.

Examples: 23,212, and 2p are all negative numbers.

Use Your Vocabulary

7. Write a number to represent each situation.

The temperature is 4 degrees You owe your brother A worker’s hourly pay below zero. eight dollars. increases by $.50.

Draw a line from each negative number in Column A to its opposite in Column B.

Column A Column B

8. 212 17

9. 2335 1

2

10. 217 335

The symbol for

is

negative

353 199

4

24

3

2$ 8 $.50

HSM11A1MC_0701.indd 194 2/14/09 5:56:30 AM

Prentice Hall Algebra 1 • Teaching ResourcesCopyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.

9

Name Class Date

For every nonzero number a, a0 5 1.

For every nonzero number a and integer n, a2n 51

an . In other words, when the

exponent is negative, raise the reciprocal of the base to the opposite of the exponent.

Problem

What is the simplifi ed form of each expression?

a. 3.90 5 1 Since the exponent is 0 but the base of the expression is 3.9, which is not 0, the expression has a value of 1.

b. 922 51

92 The exponent is negative, so raise the reciprocal of 9, or 19 , to the exponent 2(22), or 2.

51

81 Simplify.

Problem

What is the simplifi ed form of 7b23

a2 using only positive exponents?

7b23

a2 57

a2 ? b23 Rewrite the expression as a product of factors with positive exponents and factors with negative exponents.

57

a2 ?1

b3 Rewrite the factor with the negative exponent by raising the reciprocal of the base to a positive exponent.

57

a2 b3 Simplify by multiplying.

7-1 ReteachingZero and Negative Exponents

Prentice Hall Algebra 1 • Teaching ResourcesCopyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.

1

Name Class Date

7-1 ELL SupportZero and Negative Exponents

Complete the vocabulary chart by fi lling in the missing information.

Word or Word Phrase

Defi nition Picture or Example

base A number used as a repeated factor. 63 5 6 3 6 3 6

Th e base is 6.

exponent 63 5 6 3 6 3 6

Th e exponent is 3.

zero as an exponent

For every nonzero number a, a0 5 1.

negative exponent

For every nonzero number a and integer n, a2n 5

1an.

exponential expression

5x

reciprocal 1x3, x3

23, 32

simplest form An algebraic expression is in simplest form when it is has no like terms, negative exponents, or parentheses.

The number that tells how many times a base is to be used as a repeated factor.

A mathematical expression consisting of a constant raised to a power.

50 5 1

622 5 162

4a22b4 5 4b4

a2

3a2 1 2a 2 5ab

A number and its reciprocal have a product of 1.

Intervention•Reteaching(2pages)Providesreteachingandpracticeexercisesforthekeylessonconcepts.Usewithstrugglingstudentsorabsentstudents.

• English Language Learner SupportHelpsstudentsdevelopandreinforcemathematicalvocabularyandkeyconcepts.

Differentiated Remediation

0–234

All-in-One Resources/OnlineEnglish Language Learner Support

All-in-One Resources/OnlineReteaching

419A Lesson Resources

Additional Instructional SupportAlgebra 1 CompanionStudentscanusetheAlgebra 1 Companionworktext(4pages)asyouteachthelesson.UsetheCompaniontosupport

• NewVocabulary

• KeyConcepts

• GotItforeachProblem

• LessonCheck

ELL SupportFocus on CommunicationHavestudentsmakeatwo-columntable.Labelonecolumn“ZeroExponent”andtheother“NegativeExponent.”Havestudentswriteanexampleofeachinthecolumns.Askvolunteersfortheirexamplestoputontheboard.Repeatthepropertyeachtimeyousimplifythepower.Forexample,say:Avaluewithazeroexponentalwaysequals1so290 5 1.Continuewithexamples,allowingstudentsachancetoexplainthepropertyusedtosimplifythepowers.Usebothnumericandalgebraicbases.

5 Assess & RemediateLesson Quiz 1. Whatisthesimplifiedformofeach

expression?

a.223

b.(5.5)0

2. Whatisthesimplifiedformofeachexpression?

a.26a2b21

b. 5y23

3. Whatisthevalueof26a23b2fora 5 22andb 5 4?

4. Do you unDERStAnD? Thenumberofhitsonawebsitedoubleseverymonth.About10,600peoplevisitedthewebsiteduringMay.Theexpression10,600•2tmodelsthenumberofvisitorsaftertmonths.Evaluatetheexpressionfort 5 0andt 5 22.Describewhateachvalueoftheexpressionrepresentsinthesituation.

ANSWERS to lESSoN quiz

1. a. 18 b.1

2. a. 26a2

b b.5y3

3. 12 4. 10,600;2,650;About10,600people

visitedthewebsiteinMay.About2,650peoplevisitedthewebsiteinMarch.

7-1 Lesson Resources

PREScRiPtioN foR REmEdiAtioNUsethestudentworkontheLessonQuiztoprescribeadifferentiatedreviewassignment.

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