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Math Help - Indices

  1. #1
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    Wink Indices

    Need some guidance!!!!!!!!


    1)Simplify the following leaving the answer in index form:

    a.(53)2

    b.(m3)3

    c.(a3b3)2

    2)Determine the value of:

    a)3-3

    b)2-4

    c)27-1/3

    d)125-2/3

    3)Solve the following:

    a)23x = 128

    b)32x = 243

    c)54x = 625

    4)a) 82x = 1

    64

    b) 252x = 1

    125

    c) 493x = 1

    343
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  2. #2
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    Hi soul

    how about you post what you have tried to solve your questions
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  3. #3
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    Quote Originally Posted by Soul View Post
    Need some guidance!!!!!!!!


    1)Simplify the following leaving the answer in index form:

    a. (53)^2

    b. (m^3)^3

    c. (a^3b^3)^2

    2)Determine the value of:

    a) 3^{-3}

    b) 2^{-4}

    c) 27^{-1/3}

    d) 125^{-2/3}


    Don't know about these......

    3)Solve the following:

    a) 2^{3x} = 128

    b) 3^{2x} = 243

    c) 5^{4x} = 625

    4)a) 8^{2x} = \frac{1}{64}

    b) 25^{2x} = \frac{1}{125}

    c) 49^{3x} = \frac{1}{343}


    Hi Soul,

    I've tried to clean up your post a little bit, but I'm not so sure about #3 and #4. Can you help us out a little here? And did I correctly interpret the first 2?
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  4. #4
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    and at first i think that question 2a) 3-3 = 0...
    silly me
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  5. #5
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    You are right, but the number changes when I post them, for question 3
    a)23x = 128
    b)32x = 243
    c)54x = 625

    4)a) 82x = 1
    64
    b) 252x = 1
    125
    c) 493x = 1
    343
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  6. #6
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    Quote Originally Posted by Soul View Post
    You are right, but the number changes when I post them, for question 3
    a)23x = 128
    b)32x = 243
    c)54x = 625

    4)a) 82x = 1
    64
    b) 252x = 1
    125
    c) 493x = 1
    343
    Hi Soul,

    If you don't know the code to convert to mathematical symbols, you will have to resort to parentheses and ^ to indicate raising a value to a power. Like....

    (2)^(3x)=128

    This is interpreted as 2^{3x}=128

    For your fractions....

    (25)^(2x) = 1/25

    This is interpreted as 25^{2x}=\frac{1}{25}

    Now, I'll work a few of these and you can try the rest and let us know how well you did.

    1a. Are you sure this one is correct? Seems trivial when compared to the others.

    53^2=2809

    1b. (m^3)^3=m^{3 \cdot 3}=m^9

    2a. (3)^{-3}=\frac{1}{(3)^3}=\frac{1}{27}

    2d. (125)^{-2/3}=(5^3)^{-2/3}=(5)^{-2}=\frac{1}{(5)^2}=\frac{1}{25}

    3a. 2^{3x}=128

    2^{3x}=2^7

    3x=7

    x=\frac{7}{3}

    4a. 8^{2x}=\frac{1}{64}

    8^{2x}=\frac{1}{8^2}

    8^{2x}=8^{-2}

    2x=-2

    x=-1

    You should now be able to use these worked examples to help you with the others. Good luck.
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  7. #7
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    Quote Originally Posted by masters View Post

    53^2=2809
    i think it should be still 53^2 because the question asks in index form ?

    CMIIW
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  8. #8
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    Hey ,


    Thank you, for the tip on posting my powers and fractions, I will try using it.
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  9. #9
    A riddle wrapped in an enigma
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    Quote Originally Posted by songoku View Post
    i think it should be still 53^2 because the question asks in index form ?

    CMIIW
    You may be right, songoku, but I think maybe it's....

    (5^3)^2=5^6

    We'll have to watch and wait for the OP to tell us, won't we?
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  10. #10
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    Quote Originally Posted by masters View Post
    (5^3)^2=5^6
    Yes it makes sense and i guess this is the right question

    btw, what does OP stands for?
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  11. #11
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    Quote Originally Posted by songoku View Post
    Yes it makes sense and i guess this is the right question

    btw, what does OP stands for?
    Original Poster!
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  12. #12
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    Quote Originally Posted by Soul View Post
    Hey ,


    Thank you, for the tip on posting my powers and fractions, I will try using it.
    And, Soul, if you're planning to post on the forum a lot you will probably want to learn the LaTex code. Start here..

    http://www.mathhelpforum.com/math-help/latex-help/
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  13. #13
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    This is the right format, I just asked my tutor. (5^3)^2
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  14. #14
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    Log

    1) a) 641/2 x 271/3 x 160 =

    b) Compute:

    log232 log3243 =

    log464

    c) log25k =

    K =

    2) (x3/2)3 x √(x9)
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  15. #15
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    Quote Originally Posted by Soul View Post
    1) a) 641/2 x 271/3 x 160 =

    b) Compute:

    log232 log3243 =

    log464

    c) log25k =

    K =

    2) (x3/2)3 x √(x9)

    DO u mean something else for (a) , or else you can just get the answer from the calculator .

    For (b) , i hope u mean :

     log_2{32}-log_3{243}= log_2{2^5}-log_3{3^5}

    Can u simplify it using the log properties ? I'm sure u can .

    (c) log_25{k}=\frac{1}{2}

    Convert this to index form : 25^{\frac{1}{2}}=k
     <br /> <br />
(x^{\frac{3}{2}})^3\times\sqrt{x^9} <br />
??

    Well i guess so .

    x^{\frac{9}{2}} \cdot x^{\frac{9}{2}}


    do you see why ?
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