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    Indices Ix

    Uploaded by

    Agung Jatiariska
    This document contains an indices operations worksheet with problems involving exponent rules such as multiplication, division, powers of powers, and negative and surd indices. The worksheet covers expanding expressions, evaluating products and quotients, simplifying using exponent rules, and working with negative and surd indices. Example problems include (7x2)(2x3), (2x)2, 6c3d-2, (g3g-2)4, and (16a4b12c18d6)1/4.

    Copyright:

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

    Indices Ix

    Uploaded by

    Agung Jatiariska
    62 views5 pages
    This document contains an indices operations worksheet with problems involving exponent rules such as multiplication, division, powers of powers, and negative and surd indices. The worksheet covers expanding expressions, evaluating products and quotients, simplifying using exponent rules, and working with negative and surd indices. Example problems include (7x2)(2x3), (2x)2, 6c3d-2, (g3g-2)4, and (16a4b12c18d6)1/4.

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    Original Title

    indices ix

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    This document contains an indices operations worksheet with problems involving exponent rules such as multiplication, division, powers of powers, and negative and surd indices. The worksheet covers expanding expressions, evaluating products and quotients, simplifying using exponent rules, and working with negative and surd indices. Example problems include (7x2)(2x3), (2x)2, 6c3d-2, (g3g-2)4, and (16a4b12c18d6)1/4.

    Copyright:

    © All Rights Reserved
    Download as DOC, PDF, TXT or read online from Scribd
    Download as doc, pdf, or txt
    62 views5 pages

    Indices Ix

    Uploaded by

    Agung Jatiariska
    This document contains an indices operations worksheet with problems involving exponent rules such as multiplication, division, powers of powers, and negative and surd indices. The worksheet covers expanding expressions, evaluating products and quotients, simplifying using exponent rules, and working with negative and surd indices. Example problems include (7x2)(2x3), (2x)2, 6c3d-2, (g3g-2)4, and (16a4b12c18d6)1/4.

    Copyright:

    © All Rights Reserved
    Download as DOC, PDF, TXT or read online from Scribd
    Download as doc, pdf, or txt
    of 5

    Indices Operations Worksheet #1 Name________________________Class_____

    Multiplication
    Part 1: Expand each expression then evaluate
    1.) 2 8 = _____ _____ _____ _____ _____ _____ _____ _____ = ______

    2.) 5 3 = 3.) x 5 =

    4.) 10 3 = 5.) 81  8 4 =

    6.) 7 2  7 3 = 7.) x 5  x 4 =

    8.) If two expressions have the same factor or base, what happens to the exponents when the expressions are
    multiplied?
    __________________________________________________________________________________________
    __________________________________________________________________________________________

    Example: (7x2)(2x3)

    Part 2: Simplify each expression.


    9.) 2 3  2 4 10.) 81  8 3 11.) t 4  t 4

    12.) x 5  x 9 13.) 3 4  x 3  x 5

    Part 3: Find the product of the expressions.


    14.) ( 6x 2 )( 4x 2 ) 15.) (3 x 3 y 2 )(-6 y 5 ) 16.) (5 p 3 )( m 8 p 2 )

    17.) (10 g 3 h 8 v 6 )(11gh 8 ) 18.) (4 f 9 h 3 )(5 f 6 )(3h 2 )

    19.)   2 2 x 3 y 4  (3) 2 x 4 y 4  20.) *Challenge: (3 x a y b z c )( y f z g )

    Indices Operations Worksheet #2 Name________________________Class_____


    Power to a Power
    Part 1: Expand each expression and write the product.

    1.) ( 2 3 ) 4 = _________ __________ _________ _________ = ____________

    2.) ( p 2 ) 5 =

    3.) ( x m ) 2 =

    4.) ( 2 3 x ) 2 =

    5.) What is the fast way to simplify when you raise an exponent to another power (or what can you do instead of
    expanding)?
    __________________________________________________________________________________________
    __________________________________________________________________________________________

    Part 2: Find the product. Expand if it helps you.


    6.) (2 x ) 2 7.) (10 2 ) 3

    8.) ( 3 2 x 6 ) 5 9.) (7 j 2 ) 3

    10.) (8n 2 p ) 3 11.) 2 (3a 2 ) 3

    2
     8x 2 
    2
    12.) (xy ) ( x y ) 2 2 2
    13.)  2 
     2x 

    5 2
     3x 2
      3x 
    14.)  2 
     15.)  2 
     2y   4x 
    Indices Operations Worksheet #3 Name ______________________ Class_____
    Division
    Part 1: Expand each expression to find the quotient.
    24
    1.) 3 = = _______________
    2

    32 55
    2.) = = _______________
    3  52

    x8
    3.) =
    x3

    23 x 3 y 4
    4.) =
    2  xy 2 z

    5.) Explain why you can subtract exponents when you are dividing two things with the same base.
    __________________________________________________________________________________________
    __________________________________________________________________________________________

    Part 2: Simplify to find the quotients.


    a8 711 7  b5
    6.) 3 7.) 8.)
    a 78 b4

    x 10 12  g 8  h 4 4  p 11
    9.) 4 10.) 11.)
    x g 3 h 5 8  p6

    c9 2  x3 y8 3 x 14 y 11
    12.) 13.) 14.)
    6c 4 4  y2 18 x 2

    Part 3: Negative Indices


    x5
    15.) Anything to the zero power is ______________. Show why this happens by solving this problem.
    x5
    = ________
    Rewrite without negative exponents.
    18.)  2 0  x 3 
    4
    16.) 6  c 3  d 2 17.) 6 x 4 x 10

    0
    a 12 b 3  5 x 13 y 5 z 2 
    19.) 20.)   21.) ( g 3  g 2 ) 4
     35
    2
    a 5b 5 

    3 2
     4c 5   x 8  (2 x 3 )  ( x 4 ) 2
    22.)  0
     23.)  11  24.)
     8d   y  8 x 11

    Exponent Result 25.) What is the pattern on the left side of the table with the exponents?
    44
    43
    42 26.) What is the pattern on the right side of the table with the results?

    41
    40
    4 1
    4 2

    Part 3: Surd Indices

    c
    27.) For a d can be form as ...
    ac

    For the following problems, use what you know about surd indices to simplify as much as possible and/or
    find the value of each root.
    5 2 1
    28.) 4 2 29.) (125) 3 30.) 625 5

    1 8
     1
    31.)  1 
    3 1
    32.)  x 4  33.) (16a 4b12 c18 d 6 ) 4
    8  

    1
    1 1 x y 2 z 4
    2
    34.) ab a 4b 2 6 35.) 3 3
    3
    x y z
    2 2

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