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Thread: Simplifying Fraction

  1. #1
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    Simplifying Fraction

    $\displaystyle \frac{(2ab)^-2}{2(ab)^3}$

    Can this fraction be simlified ?

    I expanded it out to:

    $\displaystyle \frac{2a^-2 + b^-2}{2a^3 + 2b^3}$

    Even in this form I can't see common factors in the numerator so does that mean this cant be simplified ?
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  2. #2
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    Where did those + signs come from? The law is $\displaystyle (ab)^n = a^nb^n$

    Can you rewrite your fraction using that rule?
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  3. #3
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    Quote Originally Posted by e^(i*pi) View Post
    Where did those + signs come from? The law is $\displaystyle (ab)^n = a^nb^n$

    Can you rewrite your fraction using that rule?

    Ok so

    $\displaystyle \frac{2a^-2 b^-2}{2a^3 2b^3}$

    Does this mean the a^-2 and a^3 be canceled ? Thats where im running in to trouble.
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  4. #4
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    $\displaystyle \dfrac{(2ab)^{-2}}{2(ab)^3} = \dfrac{1}{(2ab)^2 \cdot 2(ab)^3} =$ (?)

    finish it
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  5. #5
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    $\displaystyle \frac{1}{2*2*2a^2*b^2*a^3*b^3}$

    $\displaystyle \frac{1}{8a^2*b^2*a^3*b^3}$

    $\displaystyle \frac{1}{8a^2b^2*a^3*b^3}$

    $\displaystyle \frac{1}{8a^5b^5}$

    Am I there ?
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  6. #6
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    "There" you are!
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  7. #7
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    In the fraction above we can move (2ab)^-2 down with the denominator and change the power, I understand that is just what you have to do but I am wondering why does this work and when can we apply this method and when not ?
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  8. #8
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    Quote Originally Posted by maca404 View Post
    In the fraction above we can move (2ab)^-2 down with the denominator and change the power, I understand that is just what you have to do but I am wondering why does this work and when can we apply this method and when not ?
    why it works ...

    you should know that $\displaystyle \dfrac{x^a}{x^b} = x^{a-b}$

    so , what do you get if $\displaystyle a = 0$ ?


    now you have the rule ...

    $\displaystyle x^{-b} = \dfrac{1}{x^b}$

    so ...

    $\displaystyle (2ab)^{-2} = \dfrac{1}{(2ab)^2}$

    ... all day long.
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