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7-1
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7-1
Skills Practice
Practice
Multiplying Monomials
Multiplying Monomials
Determine whether each expression is a monomial. Write yes or no. Explain.
Determine whether each expression is a monomial. Write yes or no. Explain. 21a2 7b
1. ᎏ No; this involves the quotient, not the product, of variables.
2. a ⫺ b No; This is the difference, not the product, of two variables.
2. ᎏ Yes; this is the product of a number, ᎏ , and two variables.
EP4 EP4
1. 11 Yes; 11 is a real number and an example of a constant.
p2 q
3. ᎏ2 No; This is the quotient, not the product, of two variables.
5. j 3k Yes; This is the product of two variables. 6. 2a ⫹ 3b No; This is the sum of two monomials. Simplify. 7. a2(a3)(a6) a11
8. x(x2)(x7) x10 10. (ᐉ2k2)(ᐉ3k) ᐉ5k 3
11. (e2f 4)(e2f 2) e 4f 6
12. (cd2)(c3d2) c 4d 4
Simplify. 3. (⫺5x2y)(3x4) ⫺15x 6y
4. (2ab2c2)(4a3b2c2) 8a 4b 4c 4
5. (3cd4)(⫺2c2) ⫺6c 3d 4
6. (4g3h)(⫺2g5) ⫺8g 8h
冢
冣
1 3
7. (⫺15xy4) ⫺ ᎏ xy3 5x2y 7
8. (⫺xy)3(xz) ⫺x 4y 3z
冢
10. (0.2a2b3)2 0.04a 4b 6
冣
1 6
9. (⫺18m2n)2 ⫺ ᎏ mn2 ⫺54m 5n 4
冢 23 冣
11. ᎏ p
2
冢 14 冣
4 ᎏp2 9
12. ᎏ cd3
13. (0.4k3)3 0.064k 9
15. (4xy3)(3x3y5) 12x 4y 8
16. (7a5b2)(a2b3) 7a7b 5
17.
18.
19. (102)3 106 or 1,000,000
23.
8c 5d 2
20. (p3)12 p 36 22. (⫺3y)3 ⫺27y 3
21. (⫺6p)2 36p 2 (3pq2)2
(⫺2c4d)(⫺4cd)
9p 2q 4
24.
(2b3c4)2
4b 6c 8
GEOMETRY Express the area of each figure as a monomial. 25.
26.
27.
Glencoe Algebra 1
x2
cd
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
14. (5a7)(4a2) 20a 9
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
13. (2x2)(3x5) 6x7
⫺15m11
1 ᎏ c 2d 6 16
14. [(42)2]2 48 or 65,536
GEOMETRY Express the area of each figure as a monomial. 15.
(⫺5m3)(3m8)
2
16.
(Lesson 7-1)
A3
9. ( y2z)(yz2) y3z3
1 2
17. 5x 3
3ab 2
6ac 3
6a 2b 4
4a 2c
18a 3b 6
(25x 6)
12a 3c 4
GEOMETRY Express the volume of each solid as a monomial. 18.
19.
n
3h 2
mn 3 m 3n
20.
3g 7g 2
3h 2 3h 2
27h 6
m 4n 5
(63g 4)
21. COUNTING A panel of four light switches can be set in 24 ways. A panel of five light switches can set in twice this many ways. In how many ways can five light switches be set? 25 or 32
4p
x5
x7 Chapter 7
cd
22. HOBBIES Tawa wants to increase her rock collection by a power of three this year and then increase it again by a power of two next year. If she has 2 rocks now, how many rocks will she have after the second year? 26 or 64
9p 3
c 2d 2
18p 4 8
Answers
Glencoe Algebra 1
Chapter 7
9
Answers
873950 Alg1 CH07 873950 Alg1 CH07
4. y Yes; Single variables are monomials.
b3c2 2
Lesson 7-1
Chapter 7
NAME ______________________________________________ DATE______________ PERIOD _____
Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
7-2
NAME ______________________________________________ DATE______________ PERIOD _____
7-2
Practice Dividing Monomials
Dividing Monomials 1. CHEMISTRY The nucleus of a certain atom is 10⫺13 centimeters across. If the nucleus of a different atom is 10⫺11 centimeters across, how many times as large is it as the first atom? 100
Simplify. Assume that no denominator is equal to zero. a4b6 2. ᎏ ab3
or 4096
m5np m p
冢 4f3hg 冣 3
冢 7p6ws 冣
64f 9g 3 ᎏ 27h18
3
5
8. ᎏ 6 3
⫺2
ᎏ3 9. ᎏ 5 ⫺
11. p(q⫺2)(r⫺3) ᎏ 2 3
冢 43 冣
49 ᎏ 9
14. ᎏ
⫺4
1 144
12. 12⫺2 ᎏ
22r3s2 11r s
81 ᎏ 256
8c3d2f 4 17. ᎏᎏ 4c⫺1d 2f ⫺3
3 ⫺ᎏ u4
1 6c
5 15. ᎏ 2 ⫺3 2rs
2c 4f 7
x⫺3y5 0 18. ᎏ 4⫺3
冢
冣
COMPUTERS For Exercises 5–7, use the following information. 2. SPACE The Moon is approximately 254 kilometers away from Earth on average. The Olympus Mons volcano on Mars stands 25 kilometers high. How many Olympus Mons volcanoes, stacked on top of one another, would fit between the surface of the Earth and the Moon?
In 1995, standard capacity for a personal computer hard drive was 40 megabytes (MB). In 2006, a standard hard drive capacity was 40 gigabytes (GB or Gig). Refer to the table below. Memory Capacity Approximate Conversions 8 bits = 1 byte
253 ⫽ 15,625
103 bytes = 1 kilobyte
1
103 kilobytes = 1 megabyte (meg)
m⫺2n⫺5 m 2 22. ᎏᎏ ᎏ (m4n3)⫺1 n 2
j ( j⫺1k3)⫺4 23. ᎏ ᎏ j 3k3 k15
q⫺1r 3 ⫺5 q10
冢 qr 冣
25. ᎏ ⫺2
7c⫺3d 3 ⫺1
冢 c de 冣
26. ᎏ 5 ⫺4
ᎏ r 25
6t 2u 4 ⫺ᎏ v9
c8 ᎏ 7d 2e 4
r4 r 21. ᎏ3 ᎏ (3r) 27
(2a⫺2b)⫺3 a 4 24. ᎏᎏ ᎏ 5a2b4 40b 7 2x3y2z ⫺2
冢 3x yz 冣
27. ᎏ 4 ⫺2
9x 2 ᎏ 4y 2z 6
28. BIOLOGY A lab technician draws a sample of blood. A cubic millimeter of the blood contains 223 white blood cells and 225 red blood cells. What is the ratio of white blood 1 cells to red blood cells? ᎏ
484
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⫺12t⫺1u5v⫺4 20. ᎏᎏ 2t⫺3uv5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
103 megabytes = 1 gigabyte (gig)
6f ⫺2g3h5 g 8h 2 19. ᎏᎏ 54f ⫺2g⫺5h3 ᎏ 9
103 gigabytes = 1 terabyte
5. The newer hard drives have about how many times the capacity of the 1995 drives? 103 or 1000
3. E-MAIL Spam (also known as junk e-mail) consists of identical messages sent to thousands of e-mail users. People often obtain anti-spam software to filter out the junk e-mail messages they receive. Suppose Yvonne’s anti-spam software filtered out 102 e-mails, and she received 104 e-mails last year. What fraction of her e-mails were filtered out? Write your answer as a monomial.
6. Predict the hard drive capacity in the year 2017 if this rate of growth continues. 40 terabytes
10⫺2
Glencoe Algebra 1
7. One kilobyte of memory is what fraction of one terabyte? ᎏ1ᎏ ⫺9
29. COUNTING The number of three-letter “words” that can be formed with the English alphabet is 263. The number of five-letter “words” that can be formed is 265. How many times more five-letter “words” can be formed than three-letter “words”? 676
Chapter 7
16
Answers
Glencoe Algebra 1
109
Chapter 7
17
⫽ 10
Glencoe Algebra 1
(Lesson 7-2)
A7
⫺15w0u⫺1 16. ᎏᎏ 5u3
36w10 ᎏ 49p12s 6
8y7z6 4y z
⫺4c2 24c
4. METRIC MEASUREMENT Consider a dust mite that measures 10⫺3 millimeters in length and a caterpillar that measures 10 centimeters long. How many times as long as the mite is the caterpillar? 105 ⫽ 100,000
Answers
冢 37 冣
6. ᎏ 2yz 6 5
p q r
1 x y
10. x3( y⫺5)(x⫺8) ᎏ 5 5
13. ᎏ
2
y
5d 2 4
5c2d3 ⫺4c d
5. ᎏ ⫺ᎏ 2
4. ᎏ mn 4
7. ᎏ 6
xy2 3. ᎏ xy
a 3b 3
EP4
84
873950 Alg1 CH07
88 1. ᎏ4 8
Word Problem Practice
Lesson 7-2
Chapter 7
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