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anonymous

  • one year ago

27^-4/3 How do I solve this?

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  1. Nnesha
    • one year ago
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    \[\huge\rm x^{-m} = \frac{ 1 }{ x^m }\] if there is a negative exponent then you should flip the fraction

  2. anonymous
    • one year ago
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    @Nnesha okay- what do I do after that?

  3. anonymous
    • one year ago
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    \[27^{-\frac{ 4 }{ 3 }} = \frac{ 1 }{ 27^\frac{ 4 }{ 3 } } = \frac{ 1 }{ \left( 27^\frac{ 1 }{ 3 } \right)^4 }\]

  4. anonymous
    • one year ago
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    And\[x^\frac{ 1 }{ 3 } = \sqrt[3]{x}\]

  5. anonymous
    • one year ago
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    I'm a bit confused with that second equation. How/when would I use that?

  6. anonymous
    • one year ago
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    Well, any time you have a fractional exponent, the denominator of the fraction is the root that is required. In other words,\[x^\frac{ n }{ m } = \sqrt[m]{x^n}\]And you have a fractional exponent in your question.

  7. anonymous
    • one year ago
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    Put simply, you can simplify \(27^\frac{1}{3}\)

  8. anonymous
    • one year ago
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    So does -4/3 get plugged into that or does 1/3

  9. anonymous
    • one year ago
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    I already converted my equation

  10. anonymous
    • one year ago
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    I'm sorry. I don't understand. Are you able to simplify\[\frac{ 1 }{ \left( 27^\frac{ 1 }{ 3 } \right)^4 }\]

  11. anonymous
    • one year ago
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    I don't think so, but I'm asking if I use the exponent -4/3 or the exponent 1/3 to plug into that rational expression

  12. mathstudent55
    • one year ago
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    This problem involves two exponent rules. 1. a negative exponent 2. a fractional exponent Here are the rules you need: Negative exponent: \(\Large a ^{-n} = \dfrac{1}{a^n} \) Fractional exponent: \(\Large a^{\frac{m}{n}} = \sqrt[n] {a^m} = \left( \sqrt[n] a \right)^m \)

  13. triciaal
    • one year ago
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    |dw:1439436483720:dw|

  14. triciaal
    • one year ago
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    |dw:1439436579962:dw|

  15. mathstudent55
    • one year ago
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    Let's use the negative exponent rule first. |dw:1439436586340:dw|

  16. triciaal
    • one year ago
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    |dw:1439436666466:dw|

  17. anonymous
    • one year ago
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    We break the fractional exponent into two parts and use the "power to a power" rule\[27^\frac{ 4 }{ 3 } = 27^{\frac{ 1 }{ 3 }\times4} = \left( 27^\frac{ 1 }{ 3 } \right)^4\]

  18. anonymous
    • one year ago
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    I understand that so far but which exponent do I use? The already converted exponent?

  19. mathstudent55
    • one year ago
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    The negative exponent is already taken care of. Now let's take care of the fractional exponent: |dw:1439436644180:dw|

  20. anonymous
    • one year ago
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    Order of operations. Calculate what 27^(1/3) is and raise that number to the 4th power.

  21. mathstudent55
    • one year ago
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    The fractional exponent has been taken care of, and now you have a cubic root and an exponent. Take the cubic root of 27. Then raise it to the 4th power.

  22. triciaal
    • one year ago
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    @ospreytriple the order will not matter you will get the same result the only operation is really multiplication

  23. anonymous
    • one year ago
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    I'm sorry...I'm on the app so the links or equations y'all are trying to show me aren't working. I can see the computerized version...

  24. anonymous
    • one year ago
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    9^4?

  25. anonymous
    • one year ago
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    @triciaal , I hope you'll agree it's a lot easier to take the cube of 27 and raise that result to the 4th power than it is to raise 27 to the 4th power and then take the cube root. Technically, you are correct of course, but there are practical concerns to consider.

  26. anonymous
    • one year ago
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    Or 3^4

  27. anonymous
    • one year ago
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    Yes. 3^4. The cube root of 27 is 3.

  28. mathstudent55
    • one year ago
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    |dw:1439437072181:dw|

  29. triciaal
    • one year ago
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    of course I agree that is fastest for this problem but I was addressing what you said about the order of operations

  30. anonymous
    • one year ago
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    I was following the order of operations as I wrote it (with brackets).

  31. anonymous
    • one year ago
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    So 81?

  32. anonymous
    • one year ago
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    @achara.the.blasian, you're almost there. What is 3^4?

  33. anonymous
    • one year ago
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    Well, don't forget, it's 1/81.

  34. anonymous
    • one year ago
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    Ohhhhh okay. So what do I do with that?

  35. mathstudent55
    • one year ago
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    |dw:1439437425872:dw|

  36. anonymous
    • one year ago
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    That's your answer. The question requires you to simplify the given expression. And you have. Good job.

  37. anonymous
    • one year ago
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    Thank you so much everyone

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