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    1 Laws of Indices: Level 1 Exercise Full Solution

    Uploaded by

    am661a
    This document provides examples and explanations of laws of indices. It includes: - Examples of simplifying expressions with indices such as a4 × a2 = a6 and (y3)2 = y6. - Examples of dividing and multiplying terms with indices. - Questions about evaluating expressions with indices. - Converting between standard form and scientific notation, such as 8000 = 8 × 103. - Simplifying expressions with fractional indices. The document covers basic laws and operations of indices through worked examples.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd

    1 Laws of Indices: Level 1 Exercise Full Solution

    Uploaded by

    am661a
    25 views6 pages
    This document provides examples and explanations of laws of indices. It includes: - Examples of simplifying expressions with indices such as a4 × a2 = a6 and (y3)2 = y6. - Examples of dividing and multiplying terms with indices. - Questions about evaluating expressions with indices. - Converting between standard form and scientific notation, such as 8000 = 8 × 103. - Simplifying expressions with fractional indices. The document covers basic laws and operations of indices through worked examples.

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    Original Title

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    This document provides examples and explanations of laws of indices. It includes: - Examples of simplifying expressions with indices such as a4 × a2 = a6 and (y3)2 = y6. - Examples of dividing and multiplying terms with indices. - Questions about evaluating expressions with indices. - Converting between standard form and scientific notation, such as 8000 = 8 × 103. - Simplifying expressions with fractional indices. The document covers basic laws and operations of indices through worked examples.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    25 views6 pages

    1 Laws of Indices: Level 1 Exercise Full Solution

    Uploaded by

    am661a
    This document provides examples and explanations of laws of indices. It includes: - Examples of simplifying expressions with indices such as a4 × a2 = a6 and (y3)2 = y6. - Examples of dividing and multiplying terms with indices. - Questions about evaluating expressions with indices. - Converting between standard form and scientific notation, such as 8000 = 8 × 103. - Simplifying expressions with fractional indices. The document covers basic laws and operations of indices through worked examples.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 6

    1

    Laws of Indices

    Level 1 Exercise Full Solution


    1

    (a)
    (b)
    (c)

    a 4 a 2 = a 4+ 2 = a6
    y 5 y 4 = y 5 4 = y
    ( y 3 ) 2 = y 32 = y 6

    (d)

    x 2
    x2
    x2
    )
    =
    =
    y2
    y 2 2 y 4

    (e)

    x7
    x7
    x 7
    ) y5 = 7 y5 = 2
    y
    y
    y

    (f)

    ( x 2 y 3 ) ( x3 y 2 )2 = ( x 2 y 3 ) ( x 6 y 4 ) = x 2 6 y 3 4 =

    (a)
    (b)

    4 7 4 7 = 4 7 7 = 4 0 = 1
    2 2 2 3 = 2 2( 3 ) = 2 5 = 32

    (c)

    3 1 3 2 = 3( 1 )+( 2 ) = 3 3 =

    (a)

    a 4 a 2 = a 42 = a 2

    (b)

    a 6 a 5 = a 6 5 = a 11 =

    1
    a11

    (c)

    ( a 2 ) 3 = a ( 2 )3 = a 6 =

    1
    a6

    (d)

    a 3 a 2 a 1 = a 3 2 + ( 1 ) = a 6 =

    (a)
    (b)
    (c)
    (d)

    1
    27

    35
    1
    = 35 6 = 3 1 =
    6
    3
    3
    4 3
    43
    (2 )
    2
    212
    =
    =
    =1
    ( 2 2 ) 6 2 26 212
    ( 8 3 ) 2 8 32
    1
    = 5+ 2 = 8 6 7 = 8 1 =
    5
    2
    8
    8 8
    8
    5 2
    7
    10 7
    3
    ( 2 ) 2 = 2
    =2 =8

    Hong Kong Exam & Research

    1
    a6

    1
    x4 y

    (a)

    (b)

    3x = 9
    3 x = 32
    x=2
    1
    9 x =
    27
    ( 32 ) x =

    1
    33

    3 2 x = 3 3
    2x = 3
    3
    x=
    2
    (a)

    a x 5 = a 4
    x5 = 4
    x=9

    (b)

    a3x = a9
    3x = 9
    x=3

    (a)
    (b)

    8 10 2 = 800
    6.3 103 = 6300

    (a)
    (b)

    5 10 2 = 0.05
    7.5 10 3 = 0.0075

    (a)
    (b)

    8000 = 8 103
    0.074 = 7.4 10 2

    10

    (a)

    5 3 =

    (b)

    13
    1
    1
    = 3 =
    27
    3
    3

    1
    1
    =
    3
    125
    5

    Hong Kong Exam & Research

    Level 2 Exercise Full Solution


    11

    12

    13

    (a)

    52 ( 22 )3 42 = 52 223 2 2 = 52 22 = 100

    (b)

    9 2 3 = 3 4 +1 = 3 3 =

    (c)

    (d)

    3 2 ( 42 190 ) = 3 2 42 =

    (a)

    3x 2 4( x 2 ) 3 2 ( x 3 ) 3 = 3x 2 4 x 6 2 x 9 = 24 x 17

    (b)

    ( 3a 2 ) 2 ( 6a 4 )3 32 a 4 63 a12 9 216 4 +12 6


    =
    =
    a
    = 6a10
    3 2
    2 6
    ( 18a )
    18 a
    324

    (a)

    ( 4 2 b 6 )( 2 3 b 3 ) 2 = ( 2 4 b 6 )( 2 6 b 6 ) = 2 2 = 4

    (b)

    ( a 2b 2 )3
    a 6b 6
    b9
    8 9
    a
    b
    =
    =
    =
    ( a 2b 3 ) 1 a 2b 3
    a8

    (c)

    4a 2 b 3 ( 2abc 3 ) = 4a 2 b 3 4a 2 b 2 c 6 =

    (d)

    a3 b3
    2 2
    b a

    1
    27

    3 0
    5
    5
    5
    125
    ) ( ) 3 = 1 ( ) 3 = ( )3 =
    5
    3
    3
    3
    27

    16
    9

    4a 2 b 3
    1
    = 5 6
    2 2 6
    4a b c
    b c

    a 6 b 3 a 6 a 2 a 62 a 4

    =
    =
    b
    b 4 a 2 b 4 b 3 b 4 3

    (e)
    ( a 10 bc 20 ) 0 ( a 3 b 2 ) 3 = 1 a 3( 3 ) b ( 2 )( 3 )
    = 1 a 9b 6
    1
    = 9 6
    a b
    a9
    = 6
    b

    (f)

    ( 6a 2 b 5 ) 2 ( 2a ) 3 ( 3b 2 ) 2 = 36a 4 b10 ( 8a 3 9b 4 )
    36a 4 b10
    72a 3b 4
    1
    = a 43 b10 4
    2
    a 7b6
    =
    2
    6
    b
    = 7
    2a
    =

    Hong Kong Exam & Research

    14

    (a)

    10 x = 0.01 =

    1
    1
    = 2 = 10 2
    100 10

    x=2
    (b)

    32 x =

    1
    1
    1
    = 3 4 = 12 = 3 12
    4
    27
    (3 )
    3

    2 x = 12
    x=6
    15

    2 x + 2 2 x = 48
    2 x 2 2 2 x = 48
    2 x ( 4 1 ) = 48
    3( 2 x ) = 48
    2 x = 16
    2 x = 24
    x=4

    16

    4.9 107 8.3 109 = 4.9 8.3 107 + 9 = 40.67 1016 = 4.067 1017

    17

    Number of seconds in a week


    = 7 24 60 60
    = 604800
    = 6.048 10 5

    Hong Kong Exam & Research

    MC Exercise Full Solution


    1

    A
    Number of minutes = 60 24 9 = 12960 = 1.296 10 4

    B
    p1
    1
    =
    q
    pq

    (1)

    p1 q =

    (1) is not true

    (2)

    p

    q

    (3)

    (2) is true
    p 0 q 0 = 1 1 = 1

    (3) is not true

    p 3
    = p 3q 3
    q 3

    C
    2 4 4 2 = 2 4 ( 2 2 ) 2 = 2 4 2 4 = 2 4+ 4 = 2 8

    A
    9 2 a = 3b
    ( 3 2 ) 2 a = 3b
    3 4 a = 3b
    4a = b
    b
    4
    a 1
    =
    b 4

    a=

    C
    3 n +1 + 3 n 1 3 n 3 + 3 n 3 1
    =
    3 n 1
    3n 3 1
    1
    3n ( 3 + )
    3
    =
    1
    n
    3
    3
    10 1
    =

    3 3
    = 10

    Hong Kong Exam & Research

    0.157 = 1.57 10 2 x
    1.57 10 1 = 1.57 10 2 x
    1 = 2x
    x=

    1
    2

    Hong Kong Exam & Research

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