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Math Help - Need Help Exponents Due Tomorow

  1. #1
    TH1
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    Need Help Exponents Due Tomorow

    Simplify use only positive exponents in your final answers

    (-3x^2y)^3 (-3x^-3y)^2

    (5a^-1b^2)^-2 / 125a^5b^-3

    (8x^6y^-3)^1/3 / (2xy)^3

    Any help would be greatly appreciated
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by TH1 View Post
    Simplify use only positive exponents in your final answers

    (-3x^2y)^3 (-3x^-3y)^2

    (5a^-1b^2)^-2 / 125a^5b^-3

    (8x^6y^-3)^1/3 / (2xy)^3

    Any help would be greatly appreciated
    Do you mean this
    (-3x^{2y})^3\cdot(-3x^{-3y})^2=-3x^0=-3?
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  3. #3
    TH1
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    No since the variable y isn't suppose to be an exponent but I meant everything else
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  4. #4
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by TH1 View Post
    No since the variable y isn't suppose to be an exponent but I meant everything else
    I will show you all the tools then

    YOU apply them

    It will help you learn
    (ab)^{n}=a^{n}\cdot{b^{n}}

    a^b\cdot{a^c}=a^{b+c}

    \frac{1}{a^b}=a^{-b}

    using this last definition in conjunction with the second one we can see that

    \frac{a^c}{a^b}=a^c\cdot{a^{-b}}=a^{c-b}

    \sqrt[c]{a}=a^{\frac{1}{c}}

    Apply those..not all are used...it is up to you to figure it out...if you have any specific problems post them and we will help

    Good luck
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  5. #5
    Moo
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    Hello,

    Applying the formulas : (a^b)^c=a^{bc} and a^b a^c=a^{b+c}

    You should get the answers.

    (-3x^2 y)^3 (-3x^{-3} y)^2=(-3)^3 x^6 y^3 (-3)^2 x^{-6} y^2

    =(-3)^5 x^{6-6} y^5=(-3)^5 y^5=(-3y)^5

    Can you calculate the followings ?
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  6. #6
    TH1
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    Would the final answer be 243y^5 and what about the rest of the other questions
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  7. #7
    Moo
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    There's a - sign missing...

    It would be exactly the same method for the followings..
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  8. #8
    TH1
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    For the last one how would you do that one since the exponent is a fraction and for the second one would the answer be 25a^3b
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  9. #9
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by TH1 View Post
    For the last one how would you do that one since the exponent is a fraction and for the second one would the answer be 25a^3b
    \frac{1}{3}+3=\frac{1}{3}+\frac{9}{3}=\frac{10}{3}
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  10. #10
    TH1
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    I dont understand what you wrote since for the last one the exponent is 1/3 and I dont know what to do for that part
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  11. #11
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by TH1 View Post
    I dont understand what you wrote since for the last one the exponent is 1/3 and I dont know what to do for that part
    What do you think you do?
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  12. #12
    MHF Contributor Mathstud28's Avatar
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  13. #13
    TH1
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    For the exponent 1/3 i know you have to evaluate it but when you evaluate it on 8 would it be 8/3 or would you simplify 8 as a power of 2^3 and the answer be 2 since the 3 cancels out
    2^3 1/3
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  14. #14
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by TH1 View Post
    For the exponent 1/3 i know you have to evaluate it but when you evaluate it on 8 would it be 8/3 or would you simplify 8 as a power of 2^3 and the answer be 2 since the 3 cancels out
    2^3 1/3
    if you are talking about 8^{\frac{1}{3}}=(2^3)^{\frac{1}{3}}=2^{\frac{3}{3}  }=2^1=2 then yes
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  15. #15
    TH1
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    Thanks I have another question
    if x=1/2 evaluate the expression (-2x^-2)^3(6x)^2/ 2(-3x^-1)^3

    I have evaluated part of it without substituting x=1/2 and I have
    (-8x^-6)(36x^2)/ 2(-27x^-3) so what do I do from there
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