Algebra 1 Common Core Student Edition, Grade 8-9

3a. 343m 27 b. pp c. ^ 4a. 81y20 b. 81c16

c. 54°cJ 3 ^ 5. about 1.125 X 1010 joules of energy

Lesso n Ch eck 1. n 18 2. ^ 3. 81a2 4. 81x20

5. 1 .6 X 1011 6. 3.2 X 10 -14 7. Answers may vary.
   Sample: When you raise a power to a power you multiply
   the exponents. When you multiply powers with the same
   base, you add the exponents. 8. The second student;
   when you add like terms you add the coefficients and
   keep the same variable part. 9. Answers may vary.
   Sample: x2, (x 3 ) 3 , ( x s j 5, (x5|
   Ex e r c i se s 1 1. n 32 13. x 4 15. A- 17. z? 19. c?
   X10

21. m3 49a2 3. Xl 2 25. 6 g2 27. Qy% -X 29. XZ i 31. 32/3Bk11

33. 
    
    
    
    35. 1.024X 10 13 37. 8 X 1CT 9
    
    
    
    


34. 2.56 X 1022 41. 1.33 1 20 53 X 1025


35. 4 45. f 47. 49. -2 51. -3 53. 243x3
    55. bi 57. - 8 a 5 b 4 59. 0 61. 9 63a. The student did
    not simplify the expression inside the parentheses first,
    b. 25 65. yes; (7xyz)2 67. 3 69. 1 71. 4 73. 10; (2x)4,
    (4x2)2, (16X4)1, (—2x)4, (—4x2)2, ( A ) ”4- ( A 2)” 2'

W’-

Lesson 7-4 pp. 439-445

Go t It? 1a. y? b. d? c. 4 d. A e- y4^7

l a 1 G

2. about 169 people per square mile 3a. p b. Answers
   may vary. Sample: You can simplify within the parentheses
   first to give you (a~)4 = a-17 or you can raise the
   quotient to a power first, ( ^ ) = a~

Lesso n Ch eck 1. 4 2.

y

5. 27 cubes 6. In raising a quotient to a power, the
   exponent goes to all the factors of both the numerator and
   the denominator and in raising a product to a power, the
   exponent goes to all the factors.
   7a. Answers may vary. Sample: g 3 can be rewritten as
   J_ so9± = _L. _L
   g 3’ g7 g7 g 3
   Ex e r c i se s 9. 1 1 1. 0 1 3. 3 1 5. n 3 17. y 2 19.^


6. -X 27 m2 23. Xa°c° 25. 4 X 10 “5 27. 4.2 X 103
   29.7 X 10 -3 31. ab o u t 4 .4 X 10-2 deer per acre
   33 9. 35 81x1 37 216 3 9 262,144 5 4, ^
   64 y 4 15,625 n30 2 49x3

f—la20H"^17 4 25faia2^

X12

27 3-4m34.

625y16

81x8

| S e l e c t e d A n s w e r s

vary. Sample: 3x 2 = p which is not the reciprocal of 3x2.

67. 21 69.^8 - 48m2 71. -1 and 1 73.^1 75. 4.5 77.^4
    81. y = -x + 4
    82. y = 5 x - 2
    83. y = | x - 3
    84. y = —A x — 17
    8 5. y = | x + l
    86. y = 1. 2 5 x — 3 .7 9
    87. 60,000
    88.0.07 89.820,000 90.0.003 91.340,000

Lesson 7-2 pp. 425-431

Go t I t? 1a. 89 b. (0.5)“ 1 1 c. 95 2a. 15x14

b. -56cd2 c. -p- d. Since they have like bases,

you keep the same base and add the exponents;
xa • xb • xc = x(a+b+c) 3 _^5 7 x iq30 mo|ecules of

water 4a. 2 b. 3 c. 8 5a. 125 b. 9 c. 8 6 a. 4ci

■b. (^) rI ?3 c. , 1 0 Docio 1 3 .d.. .441_/6m4.. 5 Z
Lesso n Ch eck 1. 812 2. 6n% 3. 2.4 x 101° 4. 39,900
km 5. No; x and y are not like bases and they do not
share a common factor.^6. Sometimes; if the product ab^
is gre ater th a n 10 , then the number will not be in
scientific notation. 7. No; 4 X 3 = 12 and j + ^ ^ so
the correct result is 12 aio.
Ex e r c i se s 9. (-6)19 11. 29 13. (- 8 )°

15. 5c 10 17. x 19- ~ 24 r0mB 21. 8.84 X 107 mi


16. 5 25. 8 27. 16,384 29. 196dig5 31. 9 33. \


17. \ 37. 3.42 X 1034 molecules 39. 2.7 X 10 “8


18. 8 X 10 “8 43. I 45. -12x 6 + 40x4 47. 34


19. (2X+T)(3l) 51. (f + 3)l 53. 22.5 times 55. H


20. H 59. (3, 2) 60. (-4, -5) 61. (4, 7) 62. 18, 34, 46


21. -1,7, 13 64. - 6. 8 , - 2 2. 8 , - 3 4. 8 65. X 66. 5x


22. X 68.

Lesson 7-3 pp. 4 3 2 -4 3 8

Go t It? 1a. p 20 b. p 20 c. p 5 d. p? e. yes;

(am)n = amn = (anX 2 a. ~ b. w 3 c. s 4