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Math Help - my last 'simplify the polynomial' problem

  1. #1
    Junior Member
    Joined
    Aug 2007
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    58

    my last 'simplify the polynomial' problem

    Last one of this section of my review!


    5m^-3
    __________
    6^-1 m^-2



    What steps would I need to take to solve this?

    First I would need to do something with the 6^-1. What should I do with it, since the negative power is on the bottom?

    After that I'll want to do: -3- (-2), which would be -1, so m^-1, so I would flip that to:

    m
    ___
    1

    I think.



    any input would be greatly appreciated.
    THANKS!
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  2. #2
    MHF Contributor
    Joined
    Apr 2005
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    1,631
    If the sign of the exponent is negative, it means the number/variable/expression is in the "wrong" side of the fraction.

    2 is a fraction. It is 2/1.
    So, a^(-2) is a fraction too. It is a^(-2) / 1.
    The -2 exponent of "a" means a is in the "wrong" side of the fraction. To eliminate the negative sign, just place the "a" in its correct side. If the numerator side is the "wrong" side, then the denominator side must be the "correct" side.
    so, a^(-2) = 1 / (a^2)

    and, 3 / [5^(-m)] = 3*5^m

    and, m^(-3) / [-(3^(-m))]
    = 3^m / [-1 *m^3]
    = 3^m / [-(m^3)]

    Okay. So,

    5m^-3
    __________
    6^-1 m^-2

    = 5*(6^1)(m^2) / m^3
    = 30/m ------------------answer.
    = 30*m^(-1) ------------answer also.

    -----------------------------------------
    Or, if you don't want to be bothered by putting the expressions in their "correct" sides in the fraction, then just use the exponent rules.
    a^b * a^c = a^(b+c)
    a^b / a^c = a^(b -c)

    5m^-3
    __________
    6^-1 m^-2

    = 5*(6^1)[m^(-3 -(-2))]
    = 5(6)[m^(-1)]
    = 30m^(-1) --------------------same as above.
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  3. #3
    Junior Member
    Joined
    Aug 2007
    Posts
    58
    Quote Originally Posted by ticbol View Post
    If the sign of the exponent is negative, it means the number/variable/expression is in the "wrong" side of the fraction.

    2 is a fraction. It is 2/1.
    So, a^(-2) is a fraction too. It is a^(-2) / 1.
    The -2 exponent of "a" means a is in the "wrong" side of the fraction. To eliminate the negative sign, just place the "a" in its correct side. If the numerator side is the "wrong" side, then the denominator side must be the "correct" side.
    so, a^(-2) = 1 / (a^2)

    and, 3 / [5^(-m)] = 3*5^m

    and, m^(-3) / [-(3^(-m))]
    = 3^m / [-1 *m^3]
    = 3^m / [-(m^3)]

    Okay. So,

    5m^-3
    __________
    6^-1 m^-2

    = 5*(6^1)(m^2) / m^3
    = 30/m ------------------answer.
    = 30*m^(-1) ------------answer also.

    -----------------------------------------
    Or, if you don't want to be bothered by putting the expressions in their "correct" sides in the fraction, then just use the exponent rules.
    a^b * a^c = a^(b+c)
    a^b / a^c = a^(b -c)

    5m^-3
    __________
    6^-1 m^-2

    = 5*(6^1)[m^(-3 -(-2))]
    = 5(6)[m^(-1)]
    = 30m^(-1) --------------------same as above.

    thanks! that totally makes sense
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