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Math Help - indices check

  1. #1
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    indices check

    Hiya i have attempted some indices questions, i was just woundering if anyone could check these to make sure im heading in the right direction with this subject. If these are wrong i would be most grateful if someone could correct me. thankyou

    simplify:


    1. 10^-1 x 64^1/2 x 8^0

    =0.8


    2. 5a^2b x 2a^1/2b

    =10a^5/8b^2



    3. 3b^1/2 x 2b^1/2 x 6b^-1

    =36b


    4. 7pq
    14p^2q^-2

    =0.5p^-1q^3


    5. (3xy)^2
    4xy^1/2

    =2.25xy^1.5


    6. √s^2t^4 x 3√8s^3t^9
    st

    =8^1/3s^2t^4


    7. 2a^1/2b^1/2c^-1/2 x 3a^3/2b^1/2c^3/2

    =6a^4/2bc


    8. (a^2b^3)^2 x a^-2b^-1

    =a^2b^8


    9. (5ab)^-2 x 15a^2b^3

    = 0.6ab


    10. 3x^1/2y^-1 x 5x^3/2y^-2

    = 15x^4/2y^-3


    11. 3√27p^6q^9
    √9pq

    = 3^5/6p^5/2q^7/2



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  2. #2
    MHF Contributor

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    Quote Originally Posted by daniel123 View Post
    Hiya i have attempted some indices questions, i was just woundering if anyone could check these to make sure im heading in the right direction with this subject. If these are wrong i would be most grateful if someone could correct me. thankyou

    simplify:


    1. 10^-1 x 64^1/2 x 8^0

    =0.8
    Correct


    [quote]2. 5a^2b x 2a^1/2b

    =10a^5/8b^2
    a^2 x a^{1/2}= a^{2+ 1/2}= a^{5/2}, not a^{5/8}.
    Was that a typo?



    3. 3b^1/2 x 2b^1/2 x 6b^-1

    =36b
    b^{1/2}b^{1/2}b^{-1}= b^{1/2+ 1/2- 1}= b^{1- 1}= b^0= 1


    4. 7pq
    14p^2q^-2

    =0.5p^-1q^3
    correct.


    5. (3xy)^2
    4xy^1/2

    =2.25xy^1.5
    Correct.


    6. √s^2t^4 x 3√8s^3t^9
    st

    =8^1/3s^2t^4
    It's not clear where the square roots end. Use parentheses.


    7. 2a^1/2b^1/2c^-1/2 x 3a^3/2b^1/2c^3/2

    =6a^4/2bc
    a^{1/2}a^{3/2}= a^{1/2+ 3/2}= a^2



    8. (a^2b^3)^2 x a^-2b^-1

    =a^2b^8
     (b^3)^2(b^{-1})= (b^6)(b^{-1})= b^{6- 1}

    ( (x^a)^b= x^{ab}, NOT x^{a^b})


    9. (5ab)^-2 x 15a^2b^3

    = 0.6ab
    a^{-2}a^2= a^{-2+ 2}= a^0= 1


    10. 3x^1/2y^-1 x 5x^3/2y^-2

    = 15x^4/2y^-3
    4/2= 2 !


    11. 3√27p^6q^9
    √9pq

    = 3^5/6p^5/2q^7/2


    Again, it is not clear where the square roots end. Use parentheses.
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