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calculusxy

  • one year ago

Question with exponents! Question attached below...

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  1. calculusxy
    • one year ago
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    \[\huge \frac{ (-xy^4)^{-4} }{ -2x^3 \times x^2y^3 }\]

  2. Jhannybean
    • one year ago
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    \[(-2x^3)(x^2y^2) \implies -2 \cdot x^{3+2} \cdot y^2 =~?\]

  3. calculusxy
    • one year ago
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    i got the answer of \[\frac{ 1 }{ 2x^9y^19 }\] but the answer key says that it's negative.. i don't know why

  4. Jhannybean
    • one year ago
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    Alright let's check each step.

  5. Jhannybean
    • one year ago
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    what would you get for : \(\color{#0cbb34}{\text{Originally Posted by}}\) @Jhannybean \[\large (-2x^3)(x^2y^2) \implies -2 \cdot x^{3+2} \cdot y^2 =~?\] \(\color{#0cbb34}{\text{End of Quote}}\)

  6. calculusxy
    • one year ago
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    \[\large -2x^5y^2\]

  7. Jhannybean
    • one year ago
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    Alright, and when you distribute the \(-4\) power into every term in the ( ), you expand it like so: \[\large (-xy^4)^{-4} \implies (-x)^{-4} \cdot (y^4)^{-4} = ~?\]

  8. calculusxy
    • one year ago
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    \[\large -x^{-4} \times y^0\]

  9. calculusxy
    • one year ago
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    which is basically like \[\large -x^{-4}\]

  10. calculusxy
    • one year ago
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    \[\large \times \] do you mean this symbol? if so, it's multiplication.

  11. Jhannybean
    • one year ago
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    be careful, you wouldnt be adding the exponents here, you'd be multiplying them. \[\large (y^4)^{-4} = y^{4( -4)}\qquad (y^4)^{-4} \ne y^{4-4}\]

  12. calculusxy
    • one year ago
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    oh yes

  13. calculusxy
    • one year ago
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    i still don't understand how you got the negative...

  14. calculusxy
    • one year ago
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    yeah or whose ever work that was posted in the 3 parts

  15. just_one_last_goodbye
    • one year ago
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    pretty fast eh? ^_^ thinking about making it a tool on OS as an extention

  16. Jhannybean
    • one year ago
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    defeats the purpose of Openstudy then.

  17. calculusxy
    • one year ago
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    can you please help me understand why it is a negative?

  18. Jhannybean
    • one year ago
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    Ok cotinuing from where we left off.

  19. Jhannybean
    • one year ago
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    I just realized theres an easier way to simplify the numerator, check this out

  20. Jhannybean
    • one year ago
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    Instead of expanding our numerator first, we can basically turn our entire term WITH the negative exponent into a positive one. \[\large (-xy^4)^{-4} \implies \dfrac{1}{(-xy^4)^4}\] you see how the negatives in the numerator would go away?

  21. Jhannybean
    • one year ago
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    So now we expand our numerator, and we get: \[\large \frac{1}{x^4y^{16}}\]

  22. Jhannybean
    • one year ago
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    Now we put it over our denominator: \[\large \dfrac{\dfrac{1}{x^4y^{16}}}{-2x^5y^3}\qquad \implies \qquad \dfrac{1}{-2x^{4+5}y^{16+3} } \]

  23. Jhannybean
    • one year ago
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    Now whether we have the negative in the numerator OR denominator, it doesnt matter, the fraction altogether is STILL negative.

  24. Jhannybean
    • one year ago
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    Do you follow, @calculusxy ?

  25. calculusxy
    • one year ago
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    i am still trying to grasp this.

  26. calculusxy
    • one year ago
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    if we have like complex fractions, then we would have to add the exponents n put it over one?

  27. Jhannybean
    • one year ago
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    The only reason we did that, was because we treated \((-xy^4)\) as like a variable... let' say all that junk \(=a\). And then... a is raised to a negative power, and how would we turn that power positive? by putting it over 1. \(a^{-1} \iff \dfrac{1}{a}\)

  28. Jhannybean
    • one year ago
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    So if we have a FRACTION in the numerator, and we're DIVIDING it by a term or terms in the denominator, we follow this rule: \[\dfrac{\dfrac{a}{b}}{c} \implies \frac{a}{bc}\]

  29. calculusxy
    • one year ago
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    okay...

  30. calculusxy
    • one year ago
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    i have one other question..

  31. calculusxy
    • one year ago
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    thanks for helping me understand that

  32. Jhannybean
    • one year ago
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    Which art are you stuck on? WE'll go from there.

  33. Jhannybean
    • one year ago
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    part*

  34. calculusxy
    • one year ago
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    so this time i am getting a negative, but it says that it's a positive. \[\large -\frac{ ba^0 \times -a^3b^3 }{ (ab^0)^{-4} }\]

  35. calculusxy
    • one year ago
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    so i got \[\large -a^7b^4\] but the answer key simply says \[\large a^7b^4\]

  36. calculusxy
    • one year ago
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    @Jhannybean

  37. calculusxy
    • one year ago
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    @jim_thompson5910

  38. calculusxy
    • one year ago
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    @jim_thompson5910 it's the second expression w/ exponents.

  39. jim_thompson5910
    • one year ago
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  40. calculusxy
    • one year ago
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    oh okay thx !

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