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Math Help - Review Material -- Exponents

  1. #1
    Mad
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    Review Material -- Exponents

    I just started Pre-Calc last week and am already stuck. I added the course late (college freshman) and consequently missed three classes. Those three classes were, apparently, focused on reviewing College Algebra.

    Now, I liked Algebra, I did. I did really well in it too but I haven't had it in four or five years. As a result, I've forgotten a lot of what I once knew. Unfortunately, the professor did a lot of the work in class but because I wasn't there, I have to get the answers myself.

    If someone could help me, I should be fine. I just need some reminders.

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

    x^2y^-4/x^-5y^-2

    [(x/y)^-2]^3

    All of the exponents are to be positive.

    I think I can do the rest of the review packet on my own.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Mad View Post
    (a^2/b^3)^-2
    reminder 1: \left( \frac xy \right)^a = \frac {x^a}{y^a}, which means, \left( \frac {x^a}{y^b} \right)^c = \frac {x^{ac}}{y^{bc}}, because...

    reminder 2: (x^a)^b = x^{ab}

    so here: \left( \frac {a^2}{b^3} \right)^{-2} = \frac {a^{2(-2)}}{b^{3(-2)}} = \frac {a^{-4}}{b^{-6}}

    now we want positive powers, so reminder 3: x^{-a} = \frac 1{x^a}, so...

    \frac {a^{-4}}{b^{-6}} = \frac {b^6}{a^4}


    x^2y^-4/x^-5y^-2
    reminder 4: \frac {x^a}{x^b} = x^{a - b}

    reminder 5: x^a \cdot x^b = x^{a + b} (of course, by \cdot i mean multiply)

    so, \frac {x^2 y^{-4}}{x^{-5}y^{-2}} = x^{2 - (-5)}y^{-4 - (-2)} = x^7y^{-2} = \frac {x^7}{y^2}

    [(x/y)^-2]^3
    try this one. i reminders i gave in the first problem should be a big help
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  3. #3
    Mad
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    y^6/x^6

    Is that right?
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Mad View Post
    y^6/x^6

    Is that right?
    yes!

    or i don't know if you would prefer to write \left( \frac xy \right)^6
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  5. #5
    Mad
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    Thanks. ^_^
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  6. #6
    Mad
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    (3a^2b^-2c^-1/27a^-1b^2c^-4)^-2

    9a^2c^10/b^8


    (2^-1x^2y^-3/4x^-2 y^-5)^-2


    I'm not quite sure what do to with that second one.


    Wait, is it 1/y^16?
    Last edited by Mad; February 11th 2008 at 06:44 PM.
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  7. #7
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    Quote Originally Posted by Mad View Post
    ... I just need some reminders.

    ...
    Try to do your question with the help of the attached brain crutch
    Attached Files Attached Files
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  8. #8
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    Quote Originally Posted by Mad View Post
    (3a^2b^-2c^-1/27a^-1b^2c^-4)^-2

    9a^2c^10/b^8 ...
    sorry but no

    (2^-1x^2y^-3/4x^-2 y^-5)^-2

    Wait, is it 1/y^16?
    #1:

    \left(\frac{3a^2 \cdot b^{-2} \cdot c^{-1}}{27a^{-1} \cdot b^2 \cdot c^{-4}}\right)^{-2} = \left(\frac19 \cdot a^3 b^{-4} c^3\right)^{-2} = 81 a^{-6} b^8 c^{-6}

    #2:

    \left(\frac{2^{-1} x^2 y^{-3}}{4x^{-2} y^{-5}}\right)^{-2} = \left(2^{-3} x^4 y^2\right)^{-2} = 2^6 x^{-8} y^{-4}
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