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Math Help - Simplification problem

  1. #1
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    Simplification problem

    Simplify:

    -( (a^2) / (b^3) )^3 (-a^2 b^2)^3

    = -( a^6 / b^9) (-a^6 b^6)

    = -a^6 * -a^6 * b^(6-9)

    = a^12 * b^-3

    Did I simplify this correctly? The difficult part is the -(a^6) and (-a^6).

    Thanks.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by shenton View Post
    Simplify:

    -( (a^2) / (b^3) )^3 (-a^2 b^2)^3

    = -( a^6 / b^9) (-a^6 b^6)

    = -a^6 * -a^6 * b^(6-9)

    = a^12 * b^-3

    Did I simplify this correctly? The difficult part is the -(a^6) and (-a^6).

    Thanks.
    The two expressions -(a^6) and (-a^6) are the same. The ones you need to worry about are -(a^6) and (-a)^6.

    Since the red negative sign doesn't show up in any parenthesis it is simply a constant factor out in front of everything. For the black negative sign think of it this way:
    (-a^2 b^2)^3 = (-1)^3 * (a^2)^3 * (b^2)^3 = -(a^2)^3 * (b^2)^3

    which is again outside of everything. So you got it right.

    -Dan
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  3. #3
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    Thanks, topsquark for the help and advise.
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