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DF001

  • one year ago

help with 7x^3y(3x^-1y^5/9x^3y^-2)^-3

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  1. DF001
    • one year ago
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    \[7x ^{3}y(\frac{ 3x ^{-1} y^5 }{ 9x ^{3}y ^{-2} })^{-3}\]

  2. DF001
    • one year ago
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    I am stuck on this question and I need help before an hour for class

  3. mathstudent55
    • one year ago
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    Is this the problem? \(\large 7x^3y \left( \dfrac{3x^{-1}y^5}{9x^3y^-2} \right) ^{-3}\)

  4. DF001
    • one year ago
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    |dw:1441208422555:dw|

  5. DF001
    • one year ago
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    yes and i am stuck on this process

  6. DF001
    • one year ago
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    The answer is 189x^9/y^20 but, i want to know how it is done

  7. mathstudent55
    • one year ago
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    We can start by simplifying the fraction inside the parentheses. Keep the exponent -3 as it is. We are first just working inside the parentheses.

  8. DF001
    • one year ago
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    How can I simplify the inside

  9. mathstudent55
    • one year ago
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    \(\large 7x^3y \left( \dfrac{3x^{-1}y^5}{9x^3y^-2} \right) ^{-3}\) \(\large =7x^3y \left( \dfrac{y^7}{3x^4} \right) ^{-3}\)

  10. mathstudent55
    • one year ago
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    A negative exponent in the denominator is a positive exponent in the numerator. A negative exponent in the numerator is a positive exponent in the denominator.

  11. mathstudent55
    • one year ago
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    Ok so far?

  12. DF001
    • one year ago
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    wait, where did the 9 go

  13. mathstudent55
    • one year ago
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    The 3 and the nine get reduced to 1/3. Now we deal with the negative exponent, -3. We make the exponent positive by flipping the fraction.

  14. mathstudent55
    • one year ago
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    \(\large = 7x^3y \left( \dfrac{3x^4}{y^7} \right) ^{3}\)

  15. mathstudent55
    • one year ago
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    |dw:1441208660696:dw|

  16. mathstudent55
    • one year ago
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    |dw:1441208697400:dw|

  17. DF001
    • one year ago
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    oh you only flip the numbers in front?

  18. mathstudent55
    • one year ago
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    When you flipped the fraction, you forgot to flip the 9 and the 3. Yes, you do flip the numbers because the numbers are also part of the numerator and denominator.

  19. DF001
    • one year ago
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    do I leave the variables alone

  20. mathstudent55
    • one year ago
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    After flipping, you can reduce the 9 and the 3 to 3 and 1, or just 3 in the numerator.

  21. mathstudent55
    • one year ago
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    Notice that your corrected figure (with the 3 and 1) are exactly what I am up to in Latex above.

  22. DF001
    • one year ago
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    |dw:1441209037907:dw|

  23. mathstudent55
    • one year ago
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    Now we raise the fraction to the 3rd power. To raise a fraction to a power, raise the numerator and the denominator to the power.

  24. mathstudent55
    • one year ago
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    \(\large = 7x^3y \cdot \dfrac{(3x^4)^3}{(y^7)^3} \) Ok?

  25. dinamix
    • one year ago
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    and he should find it 189 *(x^15/y^20) @mathstudent55

  26. mathstudent55
    • one year ago
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    Now we raise the numerator and denominator to the 3rd power by raising every factor. \(\large = 7x^3y\cdot \dfrac{3^3(x^4)^3}{y^{21}} \) \(\large = 7x^3y\cdot \dfrac{27x^{12}}{y^{21}} \) \(\large = \dfrac{7x^3y\cdot 27x^{12}}{y^{21}} \) \(\large = \dfrac{189x^{15}}{y^{20}} \)

  27. mathstudent55
    • one year ago
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    |dw:1441209750213:dw|

  28. mathstudent55
    • one year ago
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    |dw:1441209770713:dw|

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