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Math Help - Simplifying Expressions/Exponents

  1. #1
    Ash
    Ash is offline
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    Simplifying Expressions/Exponents

    Can you explain/show the process used to reach this answer?

    #1.
    (2b^4 c^-2)^5 (3b^-3 c^-4)^-2

    = (32 b^20 c^-10) (9 b^6 c^8) = 32 b^26/9c^2 , How did it turn into a
    fraction and not, 288 b^26 c^2?



    #2 I started these 2 problems and do not knows how to finish them-
    Can you show me how to do it?

    (3 b^5 c^-2)^3 / 2^-1 b^-3 c = 27 b^15 c^-6 / 2^-1 b^-3 c = ?


    (2b^-4 c)-3/ (2b^2 c^-5)^2 = -8b^12c^-3/4b^4c^-10 = ?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Ash View Post
    Can you explain/show the process used to reach this answer?

    #1.
    (2b^4 c^-2)^5 (3b^-3 c^-4)^-2

    = (32 b^20 c^-10) (9 b^6 c^8) = 32 b^26/9c^2 , How did it turn into a
    fraction and not, 288 b^26 c^2?
    the power of c was negative, that's why they put it in a denominator. remember, negative powers mean we take the inverse. so x^{-a} = \frac 1{x^a}


    \left(2b^4 c^{-2} \right)^5 \left( 3 b^{-3}c^{-4}\right)^{-2} =  \left( 32 b^{20} c^{-10} \right) \left( \frac 19 b^{6}c^8 \right)

    = \frac {32}9b^{20 + 6}c^{-10 + 8}

    = \frac {32}9 b^{26}c^{-2}

    = \frac {32b^{26}}{9c^2}
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