lesson practice a 7-1 integer exponents · 7-1 practice b integer exponents simplify. 1. 5 3 _____...

Copyright © by Holt, Rinehart and Winston. 3 Holt Algebra 1All rights reserved.

Name Date Class

LESSON

7-1Practice AInteger Exponents

Simplify.

1. 3 �2 � 1 ___ 3 2

� 1 ________ 3 · 3

� 1 ____ 9

2. 2 �4 � 1 ___ 2 4

� 1 ________________ 2 · 2 · 2 · 2

� 1 ____ 16

3. � �3 � �3 � 1 ______

� �3 � 3

� 1 ___________

�3 · �3 · �3 � 1 _____

�27

4. � �1 � �5 � 1 ______

� �1 � 5

� 1 ___________________

�1 · �1 · �1 · �1 · �1 � 1 ___

�1 � �1

5. � � 7.2 � 0 �1 6. � 4 � �3 1 ___ 64

Evaluate each expression for the given value(s) of the variable(s).

7. x �2 for x � 3 8. m 0 n �3 for m � 2 and n � 3 9. 5r �4 for r � �2

� 3 � �2 � 1 _____

� 3 � 2

� 1 ___

9 � 2 �

0

� 3 � �3

� � 1 � · 1 _____

� 3 � 3

5 � �2 �

�4

� 5 · 1 ______

� �2 � 4

� 1 ___ 27

� 5 · 1 _______________ �2 · �2 · �2 · �2

� 5 · 1 ___ 16

� 5 ___ 16

Simplify.

10. 4x �3 11. 5 ____ b �2

12. m 3 n �4 ______ p 0

4 ___ x 3

5b 2 m 3 ___ n 4

13. k �4 ____ 2 14. f 4 ____

g �1 15. r

6 t 0 ____ s �2

1 ____ 2 k 4

f 4 g r 6 s 2

16. The weight of a silver charm is 2 �2 grams.Evaluate this expression. 1 __

4 gram or 0.25 gram

17. There are about 10 4 different species of birdson Earth. Just over 1 0 3 of them are threatened.Evaluate both expressions. 10,000; 1000

a107c07-1_pr.indd 3a107c07-1_pr.indd 3 12/26/05 7:45:02 AM12/26/05 7:45:02 AMProcess BlackProcess Black


Name Date Class

LESSON

7-1Practice BInteger Exponents

Simplify.

1. 5 �3 � 1 _______

5 3

� 1 _____ 125

2. 2 �6 � 1 _______

2 6

� 1 _____ 64

3. � �5 � �2 1 ___ 25

4. � � 4 � �3 � 1 ___ 64

5. � 6 0 �1 6. � 7 � �2 1 ___ 49


7. d �3 for d � �2 8. a 5 b �6 for a � 3 and b � 2 9. � b � 4 � �2 for b � 1

� 1 __

8

243 ____ 64

1 __ 9

10. 5z –x for z � �3 and x � 2 11. � 5z � �x for z � �3 and x � 2 12. c �3 � 16 �2 � for c � 4

5 __ 9 1 ____

225 1 ______

16,384

Simplify.

13. t �4 14. 3r �5 15. s �3 ____ t �5

1 __ t 4

3 __ r 5

t 5 ___

s 3

16. h 0 ___ 3 17.

2x �3 y �2 ________

z 4 18.

4fg �5 _____

5h �3

1 __ 3 2 _______

x 3 y 2 z 4 4fh 3 ____

5g 5

19. 14a �4 _______ 20bc �1

20. a 4 c 2 e 0 _______ b �1 d �3

21. � 3g �2 hk �2

__________ � 6h 0

7c ______ 10 a 4 b

a 4 bc 2 d 3 h ______ 2 g 2 k 2

22. A cooking website claims to contain 1 0 5 recipes.Evaluate this expression. 100,000

23. A ball bearing has diameter 2 �3 inches.Evaluate this expression. 1 __

8 inch or 0.125 inch



Name Date Class

LESSON Practice CInteger Exponents7-1

Simplify.

1. 4 �2 1 ___ 16

2. 6 0 1 3. � 6 �2

� 1 ___ 36

4. � �1 � �5 �1 5. � �3 � �2 1 __ 9

6. 5 �3 1 ____ 125

7. � 7 �3 � 1 ____

343

8. � �4 � �5 � 1 _____

1024

9. � �9 � 0 1


10. x �4 y 3 for x � 2 and y � 3 11. 5r �3 s �6 for r � 3 and s � 1

27 ___ 16

5 ___ 27

12. � 3 � m � �4 for m � 6 13. � 2a �1 b �3 for a � 2 and b � 3

1 ___ 81

� 1 ___ 27

14. � �2xy � �3 for x � �2 and y � 1 __ 2 15. � 4 __

5 m � �3

for m � 10

1 __ 8 1 ____

512

Simplify.

16. x �3 1 ___ x 3

17. z 0 1 18. t �9 1 __ t 9

19. 3n �2 3 ___ n 2

20. 2 __ 3 x �4 2 ____

3 x 4 21. �a �2 � 1 ___

a 2

22. 10r �3 s 4 10 s 4 _____ r 3

23. b 3 ______ c �2 d 3

b 3 c 2 _____ d 3

24. 5x �2 y �3

________ z 0

5 _____ x 2 y 3

25. p �9 q �4

_______ r 2 s �3

s 3 ________ p 9 q 4 r 2

26. a 0 b �2 ______

c �3 d c 3 _____

b 2 d 27.

g 3 h �2 _______

k �1 j �5

g 3 kj 5 ______

h 2

28. A micrometer is an instrument that can measure the thickness of an object very accurately. One micrometer is accurate to within 1 0 �4 inches. Evaluate this expression.

1 ______ 10,000

inch or 0.0001 inch

29. An object is being measured by a micrometer. It has athickness of 6 �3 inches. Evaluate this expression.

1 ____ 216

inch or 0.00463 inch

a107c07-1_pr.indd 5a107c07-1_pr.indd 5 6/23/06 4:40:07 PM6/23/06 4:40:07 PMProcess BlackProcess Black


Name Date Class

LESSON

7-2Practice APowers of 10 and Scientific Notation

Find the value of each power of 10.

1. 10 �2 0.01 2. 1 0 3 1000

3. 1 0 0 1 4. 1 0 �5 0.00001

5. 10 �1 0.1 6. 1 0 7 10,000,000

Complete each statement to write each number as a power of 10.

7. 100,000 8. 0.0001 9. 0.001

The decimal point is 5 The decimal point is 4 The decimal point is 3

places to the right of 1, so places to the left of 1, so places to the left of 1, so

100,000 � 10 5

. 0.0001 � 1 0 �4

. 0.001 � 1 0 �3

.

Find the value of each expression.

10. 22.6 � 10 4 226,000 11. 5.28 � 1 0 �3 0.00528

12. 476.283 � 1 0 �4 0.0476283 13. 0.482 � 1 0 6 482,000

14. 0.29 � 1 0 �1 0.029 15. 6 � 1 0 4 60,000

Write each number in scientific notation.

16. 4500 4.5 � 1 0 3 17. 6,560,000 6.56 � 1 0 6

18. 0.00002 2 � 1 0 �5 19. 0.00203 2.03 � 1 0 –3

Order each list of numbers from least to greatest.

20. 2.4 � 1 0 4 9.1 � 1 0 �3 4.7 � 1 0 3 6.13 � 1 0 4 7.2 � 1 0 �3 9.2 � 1 0 3

7.2 � 10 �3 9.1 � 1 0 �3 4.7 � 1 0 3 9.2 � 1 0 3 2.4 � 1 0 4 6.13 � 1 0 4

21. 4.5 � 10 8 1.1 � 1 0 �3 4.1 � 1 0 �2 5.6 � 1 0 �2 9.2 � 1 0 8 4.2 � 1 0 8

1.1 � 1 0 �3 4.1 � 1 0 �2 5.6 � 1 0 �2

4.2 � 1 0 8 4.5 � 1 0 8 9.2 � 1 0 8

22. In 2003, the population of Virginia was about 7,390,000.Write the population in scientific notation. 7.39 � 1 0 6

23. The land area of Virginia is about 4 � 1 0 4 square miles.Write the area in standard form. 40,000 sq mi

24. In 2003, the population of the United States was about2.9 � 1 0 8 . Write the population in standard form. 290,000,000

25. The land area of the United States is about 5.98 � 10 6 square miles. Write the area in standard form. 5,980,000 sq mi



Name Date Class

LESSON

7-2Practice BPowers of 10 and Scientific Notation


1. 1 0 �3 0.001 2. 1 0 5 100,000 3. 1 0 �4 0.0001

4. 1 0 0 1 5. 1 0 7 10,000,000 6. 1 0 1 10

Write each number as a power of 10.

7. 1,000,000 1 0 6 8. 0.001 1 0 �3 9. 0.000001 1 0 �6

10. 0.00001 1 0 �5 11. 0.1 1 0 �1 12. 0.00000001 1 0 �8


13. 5.02 � 1 0 3 5020 14. 603 � 1 0 �4 0.0603

15. 52.8 � 1 0 6 52,800,000 16. 5.41 � 1 0 �3 0.00541

17. 0.03 � 1 0 �2 0.0003 18. 22.81 � 1 0 �6 0.00002281

Write each number in scientific notation.

19. 4500 4.5 � 1 0 3 20. 6,560,000 6.56 � 1 0 6

21. 0.00002 2 � 1 0 �5 22. 0.00203 2.03 � 1 0 �3

Order the list of numbers from least to greatest.

23. 3 � 1 0 2 ; 4.54 � 1 0 �3 ; 6.75 � 1 0 2 ; 8.2 � 1 0 �4 ; 9 � 1 0 �1 ; 6.18 � 1 0 �4

6.18 � 1 0 �4 ; 8.2 � 1 0 �4 ; 4.54 � 1 0 �3 ; 9 � 1 0 �1 ; 3 � 1 0 2 ; 6.75 � 1 0 2

24. 5.4 � 1 0 �3 ; 6.2 � 1 0 �1 ; 7.25 � 1 0 3 ; 6.87 � 1 0 3 ; 2.24 � 1 0 �1 ; 6.6 � 1 0 �3

5.4 � 1 0 �3 ; 6.6 � 1 0 �3 ; 2.24 � 1 0 �1 ; 6.2 � 1 0 �1 ; 6.87 � 1 0 3 ; 7.25 � 1 0 3

25. In 1970, the number of televisions sold in the United Stateswas about 1.2 � 1 0 7 . Write this number in standard form. 12,000,000

26. In 1950, about 3,880,000 households in the United Stateshad televisions. Write this number in scientific notation. 3.88 � 1 0 6

27. Find the volume of the cube shown at right. Write theanswer in both standard form and in scientific notation.

64,000,000,000 m m 3 ; 6.4 � 1 0 10 m m 3



Name Date Class

LESSON Practice CPowers of 10 and Scientific Notation7-2


1. 1 0 4 10,000 2. 1 0 0 1 3. 1 0 �2 0.01

4. 1 0 1 10 5. 1 0 �6 0.000001 6. 1 0 �1 0.1

Write each number as a power of 10.

7. 1000 � 1 0 3 8. 0.00001� 1 0 �5 9. 0.01� 1 0 �2

10. 10,000 � 1 0 4 11. 0.001� 1 0 �3 12. 10,000,000 � 1 0 7


13. 1 � 1 0 4 � 10,000 14. 2 � 1 0 4 � 20,000

15. 5.2 � 1 0 �4 � 0.00052 16. 6.2 � 1 0 7 � 62,000,000

17. 27.9 � 1 0 5 � 2,790,000 18. 14.87 � 1 0 0 � 14.87

19. 0.2 � 1 0 �6 � 0.0000002 20. 3.25 � 1 0 2 � 325

21. 14.15 � 1 0 4 � 141,500 22. 3.287 � 1 0 �6 � 0.000003287

State whether each number is written in scientific notation. If not, explain why not.

23. 45 � 1 0 �2 no; the first number is not between 1 and 10.

24. 2.6 � 5 4 no; the second number is not a power of 10.

25. 1.41 � 1 0 8 yes

Order the list of numbers from least to greatest.

26. 2.5 � 1 0 �1 ; 2.4 � 1 0 �6 ; 5 � 1 0 3 ; 1.23 � 1 0 �1 ; 2.5 � 1 0 �5 ; 3.56 � 1 0 3

2.4 � 1 0 �6 ; 2.5 � 1 0 �5 ; 1.23 � 1 0 �1 ; 2.5 � 1 0 �1 ; 3.56 � 1 0 3 ; 5 � 1 0 3

27. 4.5 � 1 0 1 ; 2.9 � 1 0 �3 ; 1.24 � 1 0 0 ; 3.58 � 1 0 �6 ; 5.5 � 1 0 �3 ; 2.19 � 1 0 �6

2.19 � 1 0 �6 ; 3.58 � 1 0 �6 ; 2.9 � 1 0 �3 ; 5.5 � 1 0 �3 ; 1.24 � 1 0 0 ; 4.5 � 1 0 1

28. The space telescope Hubble orbits the Earth every97 minutes, and travels more than 1.50 � 1 0 8 milesevery year. Write the distance traveled in standard notation. 150,000,000 mi

29. Hubble has taken many photographs of the planet Pluto.Pluto’s mass is about 14,000,000,000,000,000,000,000 kg.Write Pluto’s mass in scientific notation. 1.4 � 10 22 kg

30. Write Pluto’s mass in terms of grams.(Hint: 1 kg � 1,000 g) 1.4 � 10 25 g



Name Date Class

LESSON

7-3Practice AMultiplication Properties of Exponents

Complete each equation to show the property.

1. a m · a n � a m � n 2. � a m � n � a mn 3. � ab � n � a n b n

Simplify.

4.

7 5 · 7 8

7

5 �

8

7 13

5.

3 �2 · 3 7

3

�2 �

7

3 5

6.

x 3 · x �5

x

3 �

�5

x �2

7. a 2 · b 6 · b �2 8. n 5 · n �1 · n �3 9. r �4 · s 5 · r 6

a 2 b 4 n r 2 s 5

10. 11. 12.

13. ( 14. 15.

16. � b 4 � 2 · � b 3 � 3 · b �2 17. � a 2 � 3 · a �6 18. � c �5 � 2 · � c 3 � �2

b 15 1 1 ___ c 16

19. The volume of a cube can be found by using the formulaV � s 3 , where s represents the length of each side of thecube. Find the volume of a cube if each side is 4 a 2 b 4 .

64 a 6 b 12

� 2 3 � 4

2

3·

4

2 12

� 4 0 � 5

4 0

·5

4 0

1

� b 2 � �4

b

2·�4

b �8

1 _____

b 8

3n � 4

3

4 n

4

8 1n 4

� 2x � 3

2 3

x 3

8 x 3

� t 3 � 4 · t 3

t 3

· 4

· t 3

t

12 · t 3

t 12

� 3



Name Date Class

LESSON

7-3Practice BMultiplication Properties of Exponents

Simplify.

1. 3 4 · 3 2 2. 2 5 · 2 4 3. 2 3 · 2 5 · 2 1

3 6 or 729 2 9 or 512 2 9 or 512

4. q �6 · q �1 5. r �3 · r 4 · s �4 6. j �2 · j �4 · j 2

1 ___ q 7

r ___ s 4

1 __ j 4

7. c 5 · b �2 · c 3 8. � h 2 � 5 9. � g 4 � �2

c 8 ___ b 2

h 10

1 ___ g 8

10. � w 6 � 0 11. ( v 2 ) 5 · v 4 12. ( w 5 ) �2 · w �3

1 v 14 1 ____ w 13

13. � f 6 � �4 · � f �2 � �3

14. � a �2 � �3 · � a 5 � 2 15. � 3b � 4

1 ___ f 18

a 16 81 b 4

16. � �5k � 2 17. � � 4m � 3 18. � �3p � �2

25 k 2

�64 m 3

1 ____ 9 p 2

19. � s 4 t � 3 · � s 4 t 3 � 2 20. � a 2 b 4 � 2 · � a �2 b 3 � �1 · a 4 21. � x 3 y 2 � �4

· � x 2 y �3 � �2

s 20 t 9

a 10 b 5

1 ______ x 16 y 2

22. The pitch of a sound is determined by the number ofvibrations produced per second. The note “middle C”produces 2.62 � 1 0 2 vibrations per second. If a pianistplays middle C for 5 � 1 0 �1 seconds, how many vibrationswill occur?

1.31 � 1 0 2 or 131 vibrations



Name Date Class

LESSON Practice CMultiplication Properties of Exponents7-3

Simplify.

1. 2 3 · 2 5 2. 6 4 · 6 1 3. 5 6 · 5 �2

2 8 or 256 6 5 or 7776 5 4 or 625

4. t �4 · t �5 5. x 4 · x 2 6. s 4 · s 6 · t 3

t �9 x 6 s 10 t 3

7. � 2 4 � 2 8. � m 4 � 0 9. � y �2 � �4

2 8 or 256 1 y 8

10. m 4 · � n 2 � 3 · n �2 11. y · x 3 · � y 2 � 2 · � x 3 � 6 12. � 4x � 3

m 4 n 4 x 21 y 5 64 x 3

13. � gh � �1 14. � � 3bc � 2 15. � j 2 k 3 � 3

1 ___ gh

�9 b 2 c 2 j 6 k 9

16. � 5d � 2 · d 4 17. � 3x y 3 � �2 · � 9y � 2 18. � r �3 s 4 � 2 · � r 2 s 7 � 0

25 d 6 9 _____ x 2 y 4

s 8 ___ r 6

19. � a 2 b �2 � �3 · � a �1 b 2 � �3

20. � x 3 y �1 � 4 · � x �2 y 2 � �3 21. � � j �3 k �2 � 2 · � j 2 � 6

1 ___ a 3

x 18 ___ y 10

� j 6

___ k 4

Find the missing exponent in each expression.

22. b 4

· b 5 � b 9 23. � t 3 �

4

� t 12 24. � h 3 � �2

� 1 ___ h 6

25. Most states are irregularly shaped. However, the shapesof some western states approximate rectangles.Wyoming is nearly rectangular, with a width of about1.5 � 1 0 6 feet and a length of about 1.9 � 1 0 6 feet. What is the approximate area of Wyoming? Write your answer in scientific notation. 2.85 � 1 0 12 square feet



Name Date Class

LESSON

7-4Practice ADivision Properties of Exponents

Simplify.

1. 3 6 ___ 3 2

� 3 6 � 2 � 3 4 � 81 2. b 8 ___

b 5 � b

8 � 5 � b 3

3. t 2 __

t 7 � t

2 � 7 � t

�5 � 1 __

t 5 4. s 3 t 4 _____

� s 2 � 3 � s 3 t 4 ____

s 6 � s

3 � 6 · t

4 � t

4 ___ s 3

5. � ab � 2 ________ � a 5 b 2 � 3

1 ______ a 13 b 4

6. x 3 y _______

� x 2 y 3 � 2 1 ____

x y 5

7. 4 3 · 3 4 · 2 3 _________ 3 2 · 4 4 · 2

9 8. � 2 __ 3 � 4 � 2

4 ___

3 4 �

16 _____

81

9. � x __ 4 � 3 � x

3 ___

4 3 � x 3 ___

64 10. � 4 __

5 � �2

� � 5 _____

4 �

2

� 25

_____ 16

11. � 3ab ____ 4 c 2

� 4 81 a 4 b 4 _______ 256 c 8

12. � 2b ___ 3c

� �3 27 c 3 _____

8 b 3

13. � 3 z 3 _____ 4 x 2 y

� �4

� � 4 x 2 y ______

3 z 3 �

4

� 256 x 8 y 4

_________ 81 z 12

14. � n __ 4 � �2

· � 6 ___ 3n

� �3 � � 4 ___

n �

2

· � 3n ___

6 �

3

� 2n

Simplify. Write each answer in scientific notation.

15. � 4.5 � 1 0 6 � � � 3 � 1 0 �2 � 16. � 1.2 � 1 0 5 � � � 6 � 1 0 3 �

4.5 � 1 0 6 _________ 3 � 1 0 �2

� 4.5 ___ 3 � 1 0 6 _____

1 0 �2 1.2 � 1 0 5 _________

6 � 1 0 3 � 1.2 ___

6 � 1 0 5 ____

1 0 3

� 1.5 � 1 0 8 � 0.2 � 1 0

2

� � 2 � 1 0 �1

� � 1 0 2

� 2 � 1 0 1

17. A retired business man calculated that he earned$8.75 � 1 0 6 after working for 35 years.

a. Write the number of years in scientific notation. 3.5 � 1 0 1

b. Divide to find the average amount he earned per year.Write your answer in standard form. $250,000



Name Date Class

LESSON

7-4Practice BDivision Properties of Exponents

Simplify.

1. 6 7 ___ 6 5

� 6 7 � 5 � 6 2 � 36 2. t

12 ___ t 7

� t 12 � 7

� t 5

3. w 9 ___ w 2

4. j 2

__ j 8

5. 20 m 5 _____ 4 m 2

w 7

1 __ j 6

5 m 3

6. c 3 d 2 _____ c 2 d 5

7. � x 4 � 2 _____ � x 3 � 5

8. � s 3 t ___ st 4

� 2

c ___ d 3

1 ___ x 7

s 4 ___ t 6

9. � 2 __ 3 � �3

10. � 3a ___ 2b

� �4 11. � � �t ___

3v � �4

27 ___ 8 16 b 4 _____

81 a 4 � 81 v 4 _____

t 4

12. � 6 __ 7 � �2

· � 4s ___ 6t

� �2 13. � 3c ___

�2 � �1

� d __ 4 � �2

14. � � 3mn ____ 2 � �1

� �4

49 t 2 _____ 16 s 2

� 32 _____ 3c d 2

81 m 4 n 4 ________ 16

Simplify. Write the answer in scientific notation.

15. � 3.8 � 1 0 5 � � � 1.9 � 1 0 �6 � 16. � 2.5 � 1 0 3 � � � 5 � 1 0 �4 �

2 � 1 0 11 5 � 1 0 6

17. A textile factory produces 1.08 � 1 0 8 yards of fabric everyyear. If the factory is in operation 360 days a year, what isthe average number of yards of fabric produced each day?Give your answer in standard form.

300,000 yards

18. It takes 5 yards of fabric to manufacture a dress. If the textilefactory turned their entire yearly production of 1.08 � 10 8 yardsof fabric into dresses, how many could they make? Give your answer in scientific notation.

2.16 � 10 7 dresses



Name Date Class

LESSON Practice CDivision Properties of Exponents7-4

Simplify.

1. 6 8 ___ 6 6

2. h 4 ____ h �3

3. 2 3 · 4 3 · 5 ________ 5 2 · 2 4

6 2 or 36 h 7 32 ___ 5

4. x 5 y 2

_____ xy 3

5. m 3 n 6 ________ m 4 n 4 p 8

6. a 5 b 2 c 3 _______ a 6 b 2 c

x 4 ___ y n 2 _____ mp 8

c 2 ___ a

7. � 4 __ 7 � �2

8. � s 2 __ t 3

� 2 � 9. � � ab ___ 6c

� 5

49 ___ 16

s 4 ___ t 6

� a 5 b 5 _______ 7776 c 5

10. � � b 2 c _____ 2 d 3 f 4

� �2

11. � xy z 2 ____ �w � 5 � 12. � 1 0 3 · 1 0 2 ________

1 0 �6 � �4

� 4 d 6 f 8 ______ b 4 c 2

� x 5 y 5 z 10

________ w 5

1 ____ 1 0 44

Simplify. Write the answer in scientific notation.

13. � 6.4 � 1 0 7 � � � 1.6 � 1 0 3 � 14. � 8.1 � 1 0 �6 � � � 9 � 1 0 �15 �

4 � 1 0 4 9 � 1 0 8

15. � 2.8 � 1 0 2 � � � 7 � 1 0 �9 � 16. � 4.8 � 1 0 5 � � � 6 � 1 0 13 �

4 � 1 0 10 8 � 1 0 �9

Find the missing exponent in each equation.

17. � c 4

___ d

� �2

� d 2 ___ c 8

18. b 14 ____

b 7

� b 7 19. � s �3 ____ t 4

� �3 � s 9 t 12

20. An actor was paid $2.1 � 1 0 6 to star in a movie. If themovie was 1 hr 45 min long, what was the actor’s salaryper minute? Give your answer standard form. $20,000 per minute



Name Date Class

LESSON

7-5Practice APolynomials

Find the degree and number of terms of each polynomial.

1. 4 w 2 2. 9 x 3 � 2x 3. 4 p 5 � p 3 � p 2 � 11

Degree: 2 Degree: 3 Degree: 5

Terms: 1 Terms: 2 Terms: 4

Fill in each blank with monomial, binomial, or trinomial.

4. A trinomial is a polynomial with three terms.

5. A monomial is a polynomial with one term.

6. A binomial is a polynomial with two terms.

Write each polynomial in standard form. Then, give the leading coefficient.

7. 12 � 3 x 2 � x 3 x 2 � x � 12 3

8. g 4 � 2 g 3 � g 5 � g 5 � g 4 � 2 g 3 �1

9. k 2 � k 4 � k 3 � 1 k 4 � k 3 � k 2 � 1 1

First, classify each polynomial by its degree (linear, quadratic, cubic, or quartic). Then, classify it by its number of terms (monomial, binomial, or trinomial ).

10. 109 z 2 11. 3x � 11 12. b 3 � 2 � 2 b 4

quadratic monomial linear binomial quartic trinomial

13. Complete the table by evaluating the polynomial for each value of z.

Polynomial z � 0 z � 1 z � 2 z � �1 z � �2

2z � 3 z 2 � 3 �3 2 13 �2 5

14. The surface area of a cylinder is approximated by thepolynomial 6 r 2 � 6rh, where r is the radius andh is the height of the cylinder. Find the approximatesurface area of the cylinder at right.

72 in 2



Name Date Class

LESSON

7-5Practice BPolynomials


1. 14 h 3 � 2h � 10 2. 7y � 10 y 2 3. 2 a 2 � 5a � 34 � 6 a 4

3 2 4

3 2 4

Write each polynomial in standard form. Then, give the leadingcoefficient.

4. 3 x 2 � 2 � 4 x 8 � x 4 x 8 � 3 x 2 � x � 2 4

5. 7 � 50j � 3 j 3 � 4 j 2 �3 j 3 � 4 j 2 � 50j � 7 �3

6. 6k � 5 k 4 � 4 k 3 � 3 k 2 5 k 4 � 4 k 3 � 3 k 2 � 6k 5

Classify each polynomial by its degree and number of terms.

7. �5 t 2 � 10 8. 8w � 32 � 9 w 4 9. b � b 3 � 2 b 2 � 5 b 4

quadratic binomial quartic trinomial quartic polynomial

Evaluate each polynomial for the given value.

10. 3m � 8 � 2 m 3 for m � �1 7

11. 4 y 5 � 6y � 8 y 2 � 1 for y � �1 9

12. 2w � w 3 � 1 __ 2 w 2 for w � 2 10

13. An egg is thrown off the top of a building. Its height in meters abovethe ground can be approximated by the polynomial 300 � 2t � 4.9 t 2 ,where t is the time since it was thrown in seconds.

a. How high is the egg above the ground after 5 seconds?

187.5 m

b. How high is the egg above the ground after 6 seconds?

135.6 m



Name Date Class

LESSON Practice CPolynomials7-5


1. 5 t 5 � 60 � 3 t 3 2. 9p � 31 p 9 � 6 p 2 � 42 3. �50 � 4r � r 3 � r 2 � 4 r 5

5 9 5

3 4 5

Simplify and write each polynomial in standard form. Then, givethe leading coefficient.

4. 4 g 3 � 8g � 4 g 3 � 2 g 2 2 g 2 � 8g 2

5. 13 � 5 h 3 � h 2 � h �5 h 3 � h 2 � h � 13 �5

6. 2 � 3x � 4 � � 4x � 8 x 2 8 x 2 � 2x � 8 8

Classify each polynomial according to its degree and number of terms.

7. 6 t 3 � 54 t 4 � 1 quartic trinomial

8. 14 • 3 w 2 � w quadratic binomial

9. 4 � 4 s 2 � s � � 11 � s 7 7th degree polynomial

Evaluate each polynomial for the given value.

10. 4m � 4 � 4 m 3 for m � �2 20

11. 12 y 7 � 6 y 2 � 8 y 3 � y for y � �1 �25

12. �3a � a 3 � 1 __ 3 a 2 for a � 3 15

13. A certain company’s profit in dollars can be modeled with the polynomial

� 1 __ 2 x 2 � 100x � 200 where x is the number of items produced and sold.

a. What is the profit if they produce and sell 10 of their products? $750

b. What is the profit if they produce and sell 100 of their products? $4800

c. Evaluate the company’s profit polynomial for x � 0. What does thisnumber represent? �200

It represents how much money they will lose ($200) for notproducing or selling anything.



Name Date Class

LESSON

7-6Practice AAdding and Subtracting Polynomials

Add or subtract.

1. 3 x 3 � 4 � x 3 � 10 4 x 3 � 6

2. 6 � 12 p 5 � 3p � 8 � 8 p 5 �20 p 5 � 3p � 14

Add.

3. 2m � 4 4. 3 y 2 � y � 3 5. 4 z 3 � 3 z 2 � 8 � m � 2 � 2 y 2 � 2y � 9 � 2 z 3 � z 2 � 3

3m � 6 5 y 2 � y � 12 6 z 3 � 4 z 2 � 5

6. (10 g 2 � 3g � 10) � (2 g 2 � g � 9) 12 g 2 � 4g � 1

7. (4 x 3 � x 2 � 2x) � (3 x 3 � x 2 � 4x) 7 x 3 � 6x

Subtract.

8. 12k � 3 9. 6 s 3 � 9s � 10 10. 15 a 4 � 6 a 2 � a � (4k � 2) �(3 s 3 � 4s � 10) �(6 a 4 � 2 a 2 � a)

8k � 1 3 s 3 � 5s � 20 9 a 4 � 8 a 2

11. (11 b 2 � 3b � 1) � (2 b 2 � 2b � 8) 9 b 2 � b � 9

12. ( c 3 � c 2 � 2c) � (�3 c 3 � c 2 � 4c) 4 c 3 � 6c

13. Write a polynomial that represents the difference between themeasures of angle GEO and angle OEM.

w � 8

14. Becki is building an enclosure for her rabbits against the side of herhouse.

a. Find the difference between the lengthand the width of the enclosure.

2n � 2

b. Find the perimeter of the enclosure not includingthe side of the house.

8n � 20

c. Find the perimeter of the enclosure if she built itin the yard with out the house as a wall.

12n � 28



Name Date Class

LESSON

7-6Practice BAdding and Subtracting Polynomials

Add or subtract.

1. 3 m 3 � 8 m 3 � 3 � m 3 � 2 m 2 12 m 3 � 2 m 2 � 3

2. 2pg � p 5 � 12pg � 5g � 6 p 5 �7 p 5 �10pg � 5g

Add.

3. 3 k 2 � 2k � 7 4. 5 x 2 � 2x � 3y 5. 11 hz 3 � 3 hz 2 � 8hz __ � k � 2 __ � 6 x 2 � 5x � 6y __ � 9h z 3 � h z 2 � 3hz

3 k 2 � k � 5 11 x 2 � 3x � 9y 20h z 3 � 4h z 2 � 5hz

6. � a b 2 � 13b � 4a � � � 3a b 2 � a � 7b � 4a b 2 � 20b � 3a

7. � 4 x 3 � x 2 � 4x � � � x 3 � x 2 � 4x � 5 x 3 � 2 x 2

Subtract.

8. 12 d 2 � 3dx � x 9. 2 v 5 � 3 v 4 � 8 10. � y 4 � 6a y 2 � y � a � � �4 d 2 � 2dx � 8x � � � 3 v 5 � 2 v 4 � 8 � � � �6 y 4 � 2a y 2 � y �

16 d 2 � dx � 9x � v 5 � 5 v 4 5 y 4 � 8a y 2 � 2y � a

11. � � r 2 � 8pr � p � � � �12 r 2 � 2pr � 8p � 11 r 2 � 10pr � 9p

12. � un � n 2 � 2u n 3 � � � 3u n 3 � n 2 � 4un � �3un � 2n 2 � u n 3

13. Antoine is making a banner in the shape of a triangle. Hewants to line the banner with a decorative border. How longwill the border be?

33b � 8

14. Darnell and Stephanie have competing refreshment stand businesses.Darnell’s profit can be modeled with the polynomial c 2 � 8c � 100,where c is the number of items sold. Stephanie’s profit can be modeledwith the polynomial 2 c 2 � 7c � 200.

a. Write a polynomial that represents the difference between Stephanie’sprofit and Darnell’s profit.

c 2 � 15c � 100

b. Write a polynomial to show how much they can expect to earn if theydecided to combine their businesses.

3 c 2 � c � 300



Name Date Class

LESSON Practice CAdding and Subtracting Polynomials7-6

Add or subtract.

1. � h 6 � 4 h 5 � 3 h 4 � 2 h 5 � 9 h 6 �10 h 6 � 6 h 5 � 3 h 4

2. 6q w 4 � 9q w 3 � 13q w 4 � 14w q 3 � 7 w 4 �7q w 4 � 7 w 4 � 9q w 3 � 14 wq 3

Add.

3. � 2m � 1 4. 8y x 2 � x � 6y 5. 7 k 3 � 4z k 2 � 9zk __ � 6 m 2 � m � 2 __ � 2y x 2 � 11x � 3y __ � 5z k 3 � 10z k 2 � 8zk

6 m 2 � m � 1 10y x 2 � 10x � 9y 5 zk 3 � 7 k

3 � 6 zk

2 � zk

6. � �c b 2 � 2b � 14c � � � 3c b 2 � 3c � 3b � 2 cb 2 � b � 11c

7. � 4 a 4 � 9 a 2 � 4 a 3 � � � a 3 � 11 a 2 � 4 a 5 � 4 a 4 � 20 a 2 � 5 a 3 � 4 a 5

Subtract.

8. 13 s 2 � 2sx � 8x 9. 8 r 5 � 11u r 4 � 7 10. � x 4 � 5a x 2 � x � a � � �2 s 2 � 3sx � x � � � 13 r 5 � 2 r 4 � 12 � � � �2 x 4 � 5a x 2 � x � b �

15 s 2 � 5sx � 7x �5 r 5 � 11 ur

4 � 2 r 4 � 5 x 4 � 10a x 2 � a � b

11. � �3p � pm � m 2 � � � 2 m 2 � 13p � 5pm � �3 m 2 � 6pm � 10p

12. � a g 3 � g 2 � 2a g 3 � � � 3 a 3 g � g 2 � 4ag � 3a g 3 � 3 a 3 g � 4ag � g 2

13. Vince is going to frame the rectangular picture with dimensions shown.The frame will be x � 1 inches wide. Find the perimeter of the frame.

20x � 30

14. Mr. Watford owns two car dealerships. His profit from the first can bemodeled with the polynomial c 3 � c 2 � 2c � 100, where c is the numberof cars he sells. Mr. Watford’s profit from his second dealership can bemodeled with the polynomial c 2 � 4c � 300.

a. Write a polynomial to represent the difference of the profit at his firstdealership and the profit at his second dealership.

c 3 � 2 c 2 � 6c � 200

b. What is the total amount of profit Mr. Watford earns from both dealerships?

c 3 � 2c � 400



Name Date Class

LESSON

7-7Practice AMultiplying Polynomials

Multiply.

1. � 4x � � 5x � 2. � 3 x 2 � � 5x � 3. � 6 y 2 � � 3 y 3 �

20 x 2 15 x 3 18 y 5

4. 3 � 5x � 7 � 5. 4x � 2 x 2 � 7x � 3 �

15x � 21 8 x 3 � 28 x 2 � 12x

Fill in the blanks by multiplying the First, Inner, Outer, and Last terms. Then simplify.

6. � x � 5 � � x � 2 � 7. � x � 4 � � x � 3 �

x 2 2x 5x 10 x 2 �3x 4x �12

F O I L F O I L

Simplify: x 2 � 7x � 10 Simplify: x 2 � x � 12

Fill in the blanks below. Then simplify.

8. � x � 3 � � x 2 � 4x � 7 � � x � x 2 � 4x � 7 � � 3 � x 2 � 4x � 7 �

Distribute: x 3 4 x 2 7x � 3 x 2 12x 21

Simplify: x 3 � 7 x 2 � 19x � 21

9. � 2x � 1 � � 4 x 3 � 3 x 2 � 5 � � 2x � 4 x 3 � 3 x 2 � 5 � � �1 � 4 x 3 � 3 x 2 � 5 �

Distribute: 8 x 4 �6 x 3 10x � �4 x 3 3 x 2 �5

Simplify: 8 x 4 � 10 x 3 � 3 x 2 � 10x � 5

10. The length of a rectangle is 5 inches greater than the width.

a. Write an expression for the width of the rectangle. w

b. Write an expression for the length of the rectangle. w � 5

c. Write a simplified expression for the area of the rectangle. � Area � length � width � w 2 � 5w

d. Find the area of the rectangle when the width is3 inches. 24 i n 2

e. Find the area of the rectangle when the length is9 inches. 36 i n 2



Name Date Class

LESSON

7-7Practice BMultiplying Polynomials

Multiply.

1. � 6 m 4 � � 8 m 2 � 2. � 5 x 3 � � 4x y 2 � 3. � 10 s 5 t � � 7s t 4 �

48 m 6 20 x 4 y 2 70 s 6 t 5

4. 4 � x 2 � 5x � 6 � 5. 2x � 3x � 4 � 6. 7xy � 3 x 2 � 4y � 2 �

4 x 2 � 20x � 24 6 x 2 � 8x

21 x 3 y � 28x y 2 � 14xy

7. � x � 3 � � x � 4 � 8. � x � 6 � � x � 6 � 9. � x � 2 � � x � 5 �

x 2 � 7x � 12 x 2 � 12x � 36 x 2 � 7x � 10

10. � 2x � 5 � � x � 6 � 11. � m 2 � 3 � � 5m � n � 12. � a 2 � b 2 � � a � b �

2 x 2 � 17x � 30

5 m 3 � m 2 n� 15m � 3n

a 3 � a 2 b � a b 2 � b 3

13. � x � 4 � � x 2 � 3x � 5 � 14. � 3m � 4 � � m 2 � 3m � 5 � 15. � 2x � 5 � � 4 x 2 � 3x � 1 �

x 3 � 7 x 2 � 17x� 20

3 m 3 � 5 m 2 � 3m � 20

8 x 3 � 26 x 2 � 17x � 5

16. The length of a rectangle is 3 inches greater than the width.

a. Write a polynomial that represents the areaof the rectangle. w 2 � 3w

b. Find the area of the rectangle when thewidth is 4 inches. 28 i n 2

17. The length of a rectangle is 8 centimeters less than 3 times the width.

a. Write a polynomial that represents the areaof the rectangle. 3 w 2 � 8w

b. Find the area of the rectangle when thewidth is 10 centimeters. 220 c m 2

18. Write a polynomial to represent the volume of the rectangular prism.

1 __ 2 x 3 � 5 __

2 x 2 � 13x � 60



Name Date Class

LESSON Practice CMultiplying Polynomials7-7

Multiply.

1. � 1 __ 2 m 3 � � 6m � � 2 m 2 � 2. � �3 x 4 � � 2x � � 0.75 x 4 � 3. � 1 __

4 x 3 y 2 � � xy � � 1 __

4 x �

6 m 6 �4.5 x 9 1 ___ 16

x 5 y 3

4. 1 __ 2 x � 6 x 2 � 10x � 5 � 5. x 2 y � 3xy � 2 x 2 y � 6. 0.4x � 0.6x � 8y �

3 x 3 � 5 x 2 � 5 __ 2 x 3 x 3 y 2 � 2 x 4 y 2 0.24 x 2 � 3.2xy

7. � 2x � 1 � � x � 2 � 8. � 3x � 4 � � 2x � 5 � 9. � x 2 � 3 � � x � 4 �

2 x 2 � 5x � 2 6 x 2 � 23x � 20 x 3 � 4 x 2 � 3x � 12

10. � x 2 � y 2 � � x 2 � y 2 � 11. � x � 1 __ 2 � � x � 1 __

4 � 12. � 3 x 2 � 1 � � x � 1 �

x 4 � 2 x 2 y 2 � y 4 x 2 � 3 __ 4 x � 1 __

8 3 x 3 � 3 x 2 � x � 1

13. � x 2 � 1 � � x 2 � 4x � 3 � 14. � 5x � y � � x 2 � xy � y 2 �

x 4 � 4 x 3 � 4 x 2 � 4x � 3

5 x 3 � 6 x 2 y � 6x y 2 � y 3

15. � a � b � c � � a � b � c �

a 2 � 2ab � 2ac � b 2 � 2bc � c 2

16. The length of a rectangle is 2 inches more than 3 times the width.

a. Write a polynomial that represents the areaof the rectangle. 3 w 2 � 2w

b. Find the area of the rectangle when thewidth is 2.5 inches. 23.75 i n 2

17. Write a polynomial to represent the volume ofthe triangular prism. (The volume of a prism isequal to the area of its base times its height.)

5 x 3 � 13 ___ 2 x 2 � x � 1 __

2

18. If x � 3, what are the dimensions of the triangular prism?

7 � 4 � 14

What is the volume? 196



Name Date Class

LESSON

7-8Practice ASpecial Products of Binomials


1. � x � 5 � 2 2. � m � 3 � 2 3. � 2 � a � 2

x 2

� 2 � x � � 5 � � 5 2

m 2

� 2 � m � � 3 � � 3 2

2 2

� 2 � 2 � � a � � a 2

x 2 � 10x � 25 m 2 � 6m � 9 4 � 4a � a 2

Multiply.

4. � x � 4 � 2 5. � a � 7 � 2 6. � 8 � b � 2

x 2 � 8x � 16 a 2 � 14a � 49 64 � 16b � b 2


7. � x � 10 � 2 8. � y � 6 � 2 9. � 9 � x � 2

x 2

� 2 � x � � 10 � � 10 2

y 2

� 2 � y � � 6 � � 6 2

9 2

� 2 � 9 � � x � � x 2

x 2 � 20x � 100 y 2 � 12y � 36 81 � 18x � x 2

Multiply.

10. � y � 7 � 2 11. � b � 11 � 2 12. � 3 � x � 2

y 2 � 14y � 49 b 2 � 22b � 121 9 � 6x � x 2


13. � x � 7 � � x � 7 � 14. � 4 � y � � 4 � y � 15. � x � 2 � � x � 2 �

x 2

� 7 2

4 2

� y 2

x 2

� 2 2

x 2 � 49 16 � y 2 x 2 � 4

Multiply.

16. � x � 8 � � x � 8 � 17. � 3 � y � � 3 � y � 18. � x � 1 � � x � 1 �

x 2 � 64 9 � y 2 x 2 � 1



Name Date Class

LESSON

7-8Practice BSpecial Products of Binomials

Multiply.

1. � x � 2 � 2 2. � m � 4 � 2 3. � 3 � a � 2

x 2 � 4x � 4 m 2 � 8m � 16 9 � 6a � a 2

4. � 2x � 5 � 2 5. � 3a � 2 � 2 6. � 6 � 5b � 2

4 x 2 � 20x � 25 9 a 2 � 12a � 4 36 � 60b � 25 b 2

7. � b � 3 � 2 8. � 8 � y � 2 9. � a � 10 � 2

b 2 � 6b � 9 64 � 16y � y 2 a 2 � 20a � 100

10. � 3x � 7 � 2 11. � 4m � 9 � 2 12. � 6 � 3n � 2

9x 2 � 42x � 49 16 m 2 � 72m � 81 36 � 36n � 9 n 2

13. � x � 3 � � x � 3 � 14. � 8 � y � � 8 � y � 15. � x � 6 � � x � 6 �

x 2 � 9 64 � y 2 x 2 � 36

16. � 5x � 2 � � 5x � 2 � 17. � 10x � 7y � � 10x � 7y � 18. � x 2 � 3y � � x 2 � 3y �

25 x 2 � 4 100 x 2 � 49 y 2 x 4 � 9 y 2

19. Write a simplified expression that represents the...

a. area of the large rectangle.

36 � x 2

b. area of the small rectangle.

4 � x 2

c. area of the shaded area.

32

20. The small rectangle is made larger by adding 2 unitsto the length and 2 units to the width.

a. What is the new area of the smaller rectangle?

16 � x 2

b. What is the area of the new shaded area?

20



Name Date Class

LESSON Practice CSpecial Products of Binomials7-8

Multiply.

1. � 3x � 1 � 2 2. � 5m � 0.5 � 2 3. � 7 � 2a � 2

9 x 2 � 6x � 1 25 m 2 � 5m � 0.25 49 � 28a � 4 a 2

4. � 2x � 3y � 2 5. � 2 a 2 � 9b � 2 6. � 5 a 2 � 4 b 2 � 2

4 x 2 � 12xy � 9 y 2 4 a 4 � 36 a 2 b � 81 b 2 25 a 4 � 40 a 2 b 2 � 16 b 4

7. � b � 0.5 � 2 8. � 1 __ 4 � y 2 � 2 9. � a � 0.25 � 2

b 2 � b � 0.25 1 __ 16

� 1 __ 2 y 2 � y 4 a 2 � 0.5a � 0.0625

10. � 3 x 3 � 7 � 2 11. � 2 x 2 y � 11 � 2 12. � 1 __ 2 a 3 � 3 � 2

9 x 6 � 42 x 3 � 49 4 x 4 y 2 � 44 x 2 y � 121 1 __ 4 a 6 � 3 a 3 � 9

13. � x � 0.6 � � x � 0.6 � 14. � 1 __ 2 � y � � 1 __

2 � y � 15. � x � 0.25 � � x � 0.25 �

x 2 � 0.36 1 __ 4 � y 2 x 2 � 0.0625

16. � a 2 b � ab � � a 2 b � ab � 17. � 0.8 x 2 � y 2 � � 0.8 x 2 � y 2 � 18. � 4 x 3 y � 5x � � 4 x 3 y � 5x �

a 4 b 2 � a 2 b 2 0.64 x 4 � y 4 16 x 6 y 2 � 25 x 2

19. Write a simplified expression that represents the...

a. area of the large rectangle.

30 1 __ 4 � x 2

b. area of the small rectangle.

10 9 ___ 16

� x 2

c. area of the shaded area.

19 11 ___ 16

20. A rectangle has a length � x � 3.5 � and an areaof x 2 � 12.25. What is the width of the rectangle?

x � 3.5


lesson practice a 7-1 integer exponents · 7-1 practice b integer exponents simplify. 1. 5 3 _____...

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