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  • 7/17/2019 Aat Solutions - Ch05

    1/73

    CopyrightbyM

    cDougalLittell,adivisionofHoughtonMifflin

    Company.

    Algebra 2

    Worked-Out Solution Key

    Prerequisite Skills (p. 328)

    1. 23 and 1

    2. 4

    3. y5 ax21 bx1 c

    4.

    2

    x

    y

    21

    (1, 4)

    x51

    5.3

    x

    y

    21

    x521

    2

    (2 , 218 )1

    2

    3

    4

    6.

    1

    x

    y

    21

    (22, 8)

    x

    5

    2

    2

    7. x21 9x1 205 (x1 4)(x1 5)

    8. 2x21 5x2 35 (2x2 1)(x1 3)

    9. 9x22 645 (3x2 8)(3x1 8)

    10. 2x21x1 65 0

    x521 6 }}

    (1)22 4(2)(6)}}

    2(2) 5

    21 6}

    247}

    4 5

    21 6i}

    47}

    4

    11. 10x21 13x5 3

    10x21 13x2 35 0

    (5x2 1)(2x1 3)5 0

    5x2 15 0 or 2x1 35 0

    5x5 1 or 2x5 23

    x51

    }

    5

    or x5 23}

    2

    12. x21 6x1 25 20

    x21 6x2 185 0

    x526 6 }}

    (6)22 4(1)(218)}}

    2(1)

    526 6

    }

    108}

    2

    526 66

    }

    3}

    2

    5 23 63}

    3

    Lesson 5.1

    5.1 Guided Practice (pp. 331333)

    1. (42)35 46 Power of a power property

    5 4096

    2. (28)(28)35 (28)11 3Product of powers property

    5 (28)4

    5 4096

    3. 12}9235

    23

    }

    93 Power of a quotient property

    58

    }

    729

    4.6 p1024

    }

    9 p107 5

    6

    }

    9p102427 Quotient of powers property

    56

    }

    9

    p10211

    52

    }

    3 p1011

    Negative exponent property

    5.x26x5x35x261 51 3 Product of powers property

    =x2

    6. (7y2z5)(y24z21)5 7y21 (24)z51 (21) Product ofpowers property

    5 7y22z4

    57z4

    }

    y2

    Negative exponent property

    7. 1s3

    }

    t242

    2

    5

    (s3)2

    }

    (t24)2

    Power of a quotient property

    5s6

    }

    t28

    Power of a power property

    5s6t8 Negative exponent property

    8. 1x4y22

    }

    x3y6 2

    3

    5

    (x4y22)3

    }

    (x3y6)3 Power of a quotient property

    5x4 p3y22 p3

    }

    x3 p3y6 p3 Power of a product property

    5x12y26

    }

    x9y18

    5x1229y26218 Quotient of powers property

    5x3

    }

    y24

    Negative exponent property

    5.1 Exercises (pp. 333335)

    Skill Practice

    1. a.Product of powers property

    b.Negative exponent property

    c.Power of a product property

    2. No, 25.2 is not less then 10; the number should be

    2.523 1022.

    3. 33p325 3(31 2) Product of powers property

    5 35

    5 243 4. (422)35 426 Power of a power property

    51}

    46 Negative exponent property

    51

    }

    4096

    Chapter 5

  • 7/17/2019 Aat Solutions - Ch05

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    288

    Algebra 2

    Worked-Out Solution Key

    5. (25)(25)45 (25)(11 4) Product of powers property

    5 (25)5

    5 23125

    6. (24)25 28 Power of a power property

    5 256

    7.52

    }

    555 5(2 2 5) Quotient of powers property

    5 523

    51

    }

    53

    Negative exponent property

    51

    }

    125

    8. 13}5245

    34

    }

    54

    Power of a quotient property

    581

    }

    625

    9. 12}7223

    5223

    }

    723 Power of a quotient property

    5

    73

    }

    23

    Negative exponent property

    5343

    }

    8

    10. 93p9215 9(31 (21)) Product of powers property

    5 92

    5 81

    11.34

    }

    322

    5 342 (22) Quotient of powers property

    5 36

    5 729

    12. 12}3225

    12}3245 12}32

    251 4 Product of powers property

    5 12}3221

    53

    }

    2

    Negative exponent property

    13. 63p60p6255 631 02 5 Product of powers property

    5 622

    51

    }

    62

    Negative exponent property

    51

    }

    36

    14. 111}2225

    22511}22210

    Power of a power property

    5

    1210

    }

    2210 Power of a quotient property

    5 210 Negative exponent property

    5 1024

    15. (4.23 103)(1.53 106)5 (4.23 1.5)(1033 106)

    5 6.33 109

    16. (1.23 1023)(6.73 1027)5 (1.23 6.7)(10233 1027)

    5 8.043 10210

    17. (6.33 105)(8.93 10212)5 (6.33 8.9)(1053 10212)

    5 56.073 1027

    5 5.6073 1013 102 7

    5 5.6073 1026

    18. (7.23 109)(9.43 108)5 (7.23 9.4)(1093 108)

    5 67.683 1017

    5 6.7683 1013 1017

    5 6.7683 1018

    19. (2.13 1024)35 2.133 (1024)3

    5 9.2613 10212

    20. (4.03 103)45 4.043 (103)4

    5 2563 1012

    5 2.563 1023 1012

    5 2.563 1014

    21.8.13 1012

    }

    5.43 109 5

    8.1

    }

    5.43

    1012

    }

    109

    5 1.53 103

    22. 1.13 1023

    }

    5.53 1028

    5 1.1

    }5.5

    3 1023

    }1028

    5 0.23 105

    5 2.03 10213 105

    5 2.03 104

    23.(7.53 108)(4.53 1024)

    }}

    1.53 107 5

    (7.53 4.5)(1083 1024)

    }}

    1.53 107

    533.753 104

    }

    1.53 107

    53.3753 1013 104

    }}

    1.53 107

    53.3753 105

    }

    1.53

    107

    53.375

    }

    1.5

    3105

    }

    107

    5 2.253 1022

    24.w22

    }

    w6 5 w22 2 6 Quotient of powers property

    5 w28

    51

    }

    w8

    Negative exponent property

    25.(22y3)55 (22)5(y3)5 Power of a product property

    5 210y15 Power of a power property

    5 1024y15

    26.(p3q2)215p23q22 Power of a product property

    51

    }

    p3q2 Negative exponent property

    27.(w3x22)(w6x21)5 w31 6x221 (21) Product of powersproperty

    5 w9x23

    5w9

    }

    x3

    Negative exponent

    property

    Chapter 5, continued

  • 7/17/2019 Aat Solutions - Ch05

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    cDougalLittell,adivisionofHoughtonMifflin

    Company.

    Algebra 2

    Worked-Out Solution Key

    28.(5s22t4)235 523(s22)23(t4)23 Power of a productproperty

    51

    }

    125

    ps22(23)pt4(23) Power of a power

    property

    51

    }

    125ps6pt212

    5s6

    }

    125t12

    Negative exponent

    property

    29. 13a3b52235 (3)23(a3)23(b5)23 Power of a productproperty

    51

    }

    27

    a3(23)b5(23) Power of a power

    property

    51

    }

    27

    a29b215

    51

    }

    27a9b15 Negative exponent property

    30.x21y2

    }

    x2y215x2122y22 (21) Quotient of powers property

    5x23y3

    5y3

    }x3

    Negative exponent property

    31.3c3d

    }

    9cd215

    3

    }

    9

    c32 1d12 (21) Quotient of powers property

    5c2d2

    }

    3

    32.4r4s5

    }

    24r4s255

    4

    }

    24

    r42 4s52 (25) Quotient of powers property

    51

    }

    6

    r0s10

    51

    }

    6

    p1 ps10 Zero exponent property

    5

    s10

    }

    6

    33.2a3b24

    }

    3a5b225

    2

    }

    3

    a32 5b242 (22) Quotient of powers property

    52

    }

    3

    a22b22

    52

    }

    3a2b2

    Negative exponent property

    34.y11

    }

    4z3p

    8z7

    }

    y7 5

    8y11z7

    }

    4y7z3

    5 2y112 7z72 3 Quotient of powers property

    5 2y4z4

    35.x2y

    2

    3

    }3y2 p y

    2

    }x245

    x2y2

    1

    }

    3x24y2

    Product of powers property

    5x22 (24)y2122

    }}

    3

    Quotient of powers property

    5x6y23

    }

    3

    5x6

    }

    3y3

    Negative exponent property

    36. B;

    2x2y

    }

    6xy215

    x22 1y12 (21)

    }

    3

    5xy2

    }

    3

    37. The error is that the exponents were divided and not

    subtracted.

    x10

    }

    x2 5x102 2

    5x8

    38. The error is that the exponents were multiplied instead

    of added.

    x5px35x51 3

    5x8

    39. The error is that the bases were multiplied.

    (23)2p(23)45 (23)6

    40.A5

    }

    3}

    4

    s2 s5x

    }

    3

    5 }

    3}4 1x}322

    5

    }

    3}

    4 1x

    2

    }32

    25

    }

    3x2

    }

    4 p9

    5

    }

    3x2

    }

    36

    41. v5 r2h r = x h5x

    }

    2

    5 (x)21x}22

    5 x2px

    }

    2

    5x3

    }

    2

    42. v5 lpwph l5 2x, w55x

    }

    3

    , h5x

    5(2x)15x}32(x)

    510x3

    }

    3

    43.x15y12z85x4y7z11p?

    x15y12z8

    }

    x4y7z11

    5 ?

    x152 4y122 7z82 115 ?

    x11y5z235x11y5

    }

    z3

    5 ?

    44. 3x3y2512x2y5

    }

    ?

    ?512x2y5

    }

    3x3y2

    5 4x22 3y52 2

    5 4x21y3

    54y3

    }

    x

    Chapter 5, continued

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    cDougalLittell,adivisionofHoughtonMifflin

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    290

    Algebra 2

    Worked-Out Solution Key

    45. (a5b4)25 a14b21p?

    a5 p2b4 p25 a14b21p?

    a10b85 a14b21p?

    a10b8

    }

    a14b215 ?

    a102 14p

    b82 (21)5 a24b95b9

    }

    a

    45 ?

    46. Sample answer:

    x12x165 (x4y4)(x8y12)5 (x2y15)(x10y1)5 (x25y7)(x17y9)

    47.1}

    am5

    a0

    }

    am5 a02 m5 a2m

    48.am

    }

    an5 amp

    1}

    an

    a2np

    am5 a2n1 m5 am2 n

    Problem Solving

    49. Pacific: V5 (1.563 1014)(4.033 103)

    5 (1.563 4.03)(10143 103)

    5 6.28683 1017meters3

    Atlantic: V5 (7.683 1013)(3.933 103)

    5 (7.683 3.93)(10133 103)

    5 30.1824 3 1016

    5 3.018243 1013 1016

    5 3.018243 1