sample - mastery education · lesson 5 • simplify expressions using the laws of exponents 24...

LESSON 5 Simplify Expressions Using the Laws of ExponentsCHAPTER 1

Algebra I | End-of-Coursemasteryeducation.com22 Copying is prohibited.

GUIDED PRACTICE

Write 5�2 as a decimal.Problem 1

UNPACKING the TEKS | R A.11(B)You can simplify exponential expressions using the rules of exponents.

Rules of Exponents For all x � 0, y � 0, where a and b are real numbers

Rule 1

xaxb � xa � b

Rule 2

xa

__ xb � x

a � b

Rule 3

(xa)b � xab

Rule 4

(xy)a � xaya

Rule 5

x�a � 1

__ xa

Rule 6

x0 � 1

Rule 7 x a

_ b �

b √ __ xa � (

b √ __ x )a where a and b are integers � 1

Step 1 Use Rule 5.

5�2 �

Step 2 Write the denominator 52 as a whole number.

52 �

Step 2 Divide.

1 � 25 �

Step 1

Step 2

Step 3

So 5�2 � .Solution

So 383�3 � .Solution

Simplify 383�3 to an expression with only positive exponents.Problem 2

Step 1 Use Rule 1.

383�3 � 38 �

Step 1

Words to Knowexponential expression

exponent

9781609794408_TX_ALG_EOC_SE_Book_8-2018.indb 229781609794408_TX_ALG_EOC_SE_Book_8-2018.indb 22 8/27/2018 4:01:29 PM8/27/2018 4:01:29 PMProcess BlackProcess Black

SAMPLE

LESSON 5 • SIMPLIFY EXPRESSIONS USING THE LAWS OF EXPONENTS

masteryeducation.comChapter 1 | Polynomial and Algebraic Expressions 23Copying is prohibited.

So (4m3n4)2 � .Solution

Simplify (4m3n4)2.Problem 3

Step 1 Use Rule 4. Distribute the exponent to each factor in parentheses. Find the value of 42.

42 �

Step 1 Find the value of (m3)2. See Rule 3.

(m3)2 �

Step 1 Find (n4)2. See Rule 3.

(n4)2 �

Step 1

Step 2

Step 3

Simplify (5a )2b5

_______ 3a4b2

so that variables appear only in the numerator.Problem 4

Step 1 Use Rule 4.

(5a)2 b5 ______

3a4 b2 � 25a

2 b5 ______ 3a4 b2

Step 1 Group like terms.

( 25 ___ 3 ) ( a2 __ a4 ) ( b5 ___ b2 ) Step 1 Use Rule 2 to simplify.

( 25 ___ 3 ) ( a2 __ a4 ) ( b5 ___ b2 ) � Step 1 Rewrite as a fraction.

Step 1

Step 2

Step 3

Step 4

(5a)2b5 _______

3 a4b2 � Solution


SAMPLE

x LESSON 5 • SIMPLIFY EXPRESSIONS USING THE LAWS OF EXPONENTS

Algebra I | End-of-Coursemasteryeducation.com24 Copying is prohibited.

SHORT RESPONSE QUESTIONS1. Light travels at a speed of 1.86 � 105 miles per second. A light-year is the distance that light

travels in one year. Scientists use light-years to measure astronomical distances.

Part A Find the number of seconds in one year (365 days). Write your answer in scientific notation. Show or explain your work.

� � � �

Part B Find the number of miles in a light-year. Show or explain your work.

� � � �

2. Given the expression �3a�2, where a ≠ 0.

Part A If a is a positive number, is the expression positive or negative? Explain how you know.

Part B Write the expression using only positive exponents.


SAMPLE

masteryeducation.comChapter 1 | Polynomial and Algebraic Expressions

LESSON 5 • SIMPLIFY EXPRESSIONS USING THE LAWS OF EXPONENTS

25Copying is prohibited.

PRACTICE

1 Which expression is equivalent to (6477)�3?

A 1 _____ 612 721

B � 1 _____ 612 721

C 6174

D �3 � 64 � 77[TEKS A.11(B), DOK 2]

2 Which expression is equivalent to ( x2 � x �2 ___ 3 ) 3 ?

F 1

G x8

H x4

J x�4

[TEKS A.11(B), DOK 2]

3 Which is 2�5 written as a decimal?

A �0.10

B 0.10

C �0.03125

D 0.03125[TEKS A.11(B), DOK 1]

4 The radius of a sphere is 3.0 � 105 meters. Which is the best estimate of the volume of a sphere? Use the formula V � 4 _ 3 πr

3.

F 4.2 � 1015 m3G 4.2 � 1017 m3H 1.1 � 1015 m3J 1.1 � 1017 m3[TEKS A.11(B), DOK 2]

5 The expression 2b3c represents the length of a rectangle, and 5ab2 represents the width.

5ab2

2b3c

Which expression best represents the area of the rectangle?

A 7ab6c

B 10ab5c

C 10ab6c

D 14ab5c [TEKS A.11(B), DOK 2]

6 The world’s population is approximately 6.8 � 109 people. The population of China is approximately 1.3 � 109 people. About what percent of the world’s population lives in China?

F 5%

G 19%

H 27%

J 52%[TEKS A.1(A), A.11(B), DOK 2]

7 Which expression is equivalent to k�4 p12 _____

k2 p�2 ?

A k�6p14

B k�6p10

C k�2p14

D k�2p10


DIRECTIONS Read each question and choose the best answer. Then circle the letter for the correct answer.


SAMPLE

Algebra I | End-of-Coursemasteryeducation.com

LESSON 5 • SIMPLIFY EXPRESSIONS USING THE LAWS OF EXPONENTSx

26 Copying is prohibited.

ASSESSMENT

1 Which expression represents the quotient of (ab

2c3)3 _______

(ab2c3)�1 ?

A a2b4c6

B a4b4c4

C a3b6c8

D a4b8c12

[TEKS A.1(A), A.11(B), DOK 2]

2 The population of the United States is approximately 3.1 � 108 people. The landarea of the United States is about 3.5 � 106square miles. Which is the best estimate of the average population density in the United States?

F 0.89 people per square mile

G 8.9 people per square mile

H 89 people per square mile

J 890 people per square mile[TEKS A.1(A), A.11(B), DOK 2]

3 Which expression is equivalent to 5 __ v9

?

A 5v�9

B �5v�9

C (5v)�9

D (�5v)�9


4 Which expression is equivalent to 118 ______

(2 � 112)3 ?

F 23113 H 2�3113

G 23112 J 2�3112


5 Which of the following represents (y�1x6x3y4xy�3)

1 _ 2 in simplest form?

A 1

B x8

C x5

D x5y[TEKS A.11(B), DOK 2]

6 In the equation 9x3 ya ____

3x2 y7 � 3xy�2 , what is the

value of a?

F �14

G �5

H 5

J 14[TEKS A.11(B), DOK 3]

7 An atom has a diameter of 3.0 � 10�7 mm.5.0 � 107 atoms fit across the top of abutton. How wide, in millimeters, is the button?

Record your answer and fill in the bubbles. Be sure to use the correct place value.

[TEKS A.11(B ), DOK 2]

DIRECTIONS Read each question and choose the best answer. Then circle the letter for the correct answer.


SAMPLE

sample - mastery education · lesson 5 • simplify expressions using the laws of exponents 24...

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