Math

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simplify using the exponent law. express your answer using positive exponents only.
(x^2)^3(2x^3)^-3/(4x)^2

  • Math -

    ( x ^ 2 ) ^ 3 = x ^ 6


    ( 2 x ^ 3 ) ^ ( - 3 ) = 2 ^ ( - 3 ) * x ^ [ ( - 3 ) * ( - 3 ) ] =

    2 ^ ( - 3 ) * x ^ ( - 9 )

    1 / ( 2 ^ 3 * x ^ 9 ) = 1 / 8 x ^ 9



    3 /( 4 x )^ 2 = 3 / ( 4 ^ 2 x ^ 2 ) = 1 / 16 x ^ 2



    ( x ^ 2 )^ 3 ( 2 x ^ 3 )^ -3 / ( 4 x ) ^ 2 =

    x ^ 6 * 1 / 8 x ^ 9 * 1 / 16 x ^ 2 =

    x ^ 6 / ( 8 x ^ 9 * 16 x ^ 2 ) =

    x ^ 6 / ( 128 * x ^ 11 ) =

    x ^ 6 / ( 128 * x ^ 6 * x ^ 5 ) =

    1 / 128 x ^ 5

  • Math -

    CORRECTION:


    ( 2 x ^ 3 ) ^ ( - 3 ) = 2 ^ ( - 3 ) * x ^ [ 3 * ( - 3 ) ] =

    2 ^ ( - 3 ) * x ^ ( - 9 )

    1 / ( 2 ^ 3 * x ^ 9 ) = 1 / 8 x ^ 9

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