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anonymous

  • one year ago

x^-2+x^-4= I got x^1/2+x^1/4 but i dont remember the rules well for exponents

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  1. freckles
    • one year ago
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    x^(-2) doesn't mean x^(1/2) though you can write x^(-2) as 1/x^2

  2. freckles
    • one year ago
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    and same for the x^(-4) this is not x^(1/4)

  3. anonymous
    • one year ago
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    ohhh okay so do i multiply the exponents?

  4. Jhannybean
    • one year ago
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    \[x^{-2} -x^{-4}\] You're just looking to factor out this function?

  5. anonymous
    • one year ago
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    well for the exponents, it says to put it in A/B

  6. Jhannybean
    • one year ago
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    Oh okay, so as @freckles mentioned :)

  7. Jhannybean
    • one year ago
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    Recall that \(x^{-\#} \iff \dfrac{1}{x^{\#}}\) Therefore we can write our function over 1 to make the exponents of the variables positive :) and i made a typo, my function should have read \(x^{-2} + x^{-4}\)*

  8. anonymous
    • one year ago
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    i got that now! so do we multiply the exponents to get 1/x^8?

  9. anonymous
    • one year ago
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    i completely forgot the rules

  10. anonymous
    • one year ago
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    then how?

  11. Jhannybean
    • one year ago
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    All we can do now, is factor out the denominator.

  12. freckles
    • one year ago
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    \[x^{-2}+x^{-4}=\frac{1}{x^2}+\frac{1}{x^4}\] you can combine the fractions by finding a common denominator

  13. Jhannybean
    • one year ago
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    D'oh!

  14. Jhannybean
    • one year ago
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    I made a really big error. My mistake was in putting the function as a whole in the denominator. In order to turn each variable positive, you must treat each variable as a separate function.

  15. Jhannybean
    • one year ago
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    From what @freckles wrote, just find the greatest common denominator between \(x^2\) and \(x^4\).

  16. anonymous
    • one year ago
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    ?

  17. anonymous
    • one year ago
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    common denominator is x^4?

  18. freckles
    • one year ago
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    that is right \[x^{-2}+x^{-4} \\ \frac{1}{x^2}+\frac{1}{x^4} \\ \frac{1(x^2)}{x^2(x^2)}+\frac{1}{x^4}\] now you have the same denominator combine the fractions

  19. anonymous
    • one year ago
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    so itll be x^2/x^4 do i reduce?

  20. freckles
    • one year ago
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    you will have \[\frac{x^2+1}{x^4}\]

  21. anonymous
    • one year ago
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    wouldnt that equal to x+1/x^2

  22. freckles
    • one year ago
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    no just (x^2+1)/x^4 can't be reduced because you don't have all terms with factor x^2

  23. anonymous
    • one year ago
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    than would A/B be 2/4? cause the question asked put the exponents as A/B

  24. freckles
    • one year ago
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    what?

  25. freckles
    • one year ago
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    are you saying we are suppose to write in x^(A/B) form?

  26. anonymous
    • one year ago
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    yes

  27. freckles
    • one year ago
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    \[x^{-2}+x^{-4}=x^{\frac{-2}{1}}+x^{\frac{-4}{1}}\] there is both terms written in x^(A/B) form

  28. anonymous
    • one year ago
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    oh okay thats easier to understand

  29. anonymous
    • one year ago
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    then would it be -6

  30. freckles
    • one year ago
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    I don't get your question can you post your whole question

  31. anonymous
    • one year ago
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    simplofy the rational expression in the form of A/B. x^-2+x^-4

  32. freckles
    • one year ago
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    oh in the form A/B well we did that \[\frac{x^2+1}{x^4} \\ \text{ we have } A=x^2+1 \text{ and } B=x^4\]

  33. anonymous
    • one year ago
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    oh my god thank you!

  34. freckles
    • one year ago
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    np

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