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anonymous

  • one year ago

Rewrite in simplest radical form 1/x^-3/6. Please show each step of your process.Thank -you so much

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  1. anonymous
    • one year ago
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    @peachpi

  2. mathstudent55
    • one year ago
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    Is this the problem? |dw:1434407986067:dw|

  3. anonymous
    • one year ago
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    yes:)

  4. mathstudent55
    • one year ago
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    First, you can reduce 3/6

  5. mathstudent55
    • one year ago
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    What is the fraction - 3/6 in simplest terms?

  6. anonymous
    • one year ago
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    -1/2

  7. mathstudent55
    • one year ago
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    Correct. |dw:1434408138951:dw|

  8. mathstudent55
    • one year ago
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    Do you know how to deal with a negative exponent?

  9. mathstudent55
    • one year ago
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    Here is the rule for negative exponents: \(\Large a^{-n} = \dfrac{1}{a^n} \)

  10. anonymous
    • one year ago
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    1/x^2

  11. anonymous
    • one year ago
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    Right?

  12. mathstudent55
    • one year ago
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    No. There are two things with the exponent of x we need to deal with. 1. It is a negative exponent. 2. The exponent is a fraction. Let's deal only with the negative sign on the exponent for now.

  13. anonymous
    • one year ago
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    Ok:)

  14. mathstudent55
    • one year ago
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    Just like the rule above of negative exponents works, this one also works: \(\Large \dfrac{1}{a^{-n}} = a^n \) A negative exponent in the denominator, is a positive exponent in the numerator.

  15. mathstudent55
    • one year ago
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    Notice we have a similar thing to this last rule. We have a fraction with 1 over. Then in the denominator we have x to a negative exponent. It changes into just x to the positive exponent in the numerator, and the denominator disappears.

  16. mathstudent55
    • one year ago
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    |dw:1434408609017:dw|

  17. mathstudent55
    • one year ago
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    You see how the rule and what we have are similar?

  18. anonymous
    • one year ago
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    Yes

  19. anonymous
    • one year ago
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    But that wouldn't be our final answer, right?

  20. mathstudent55
    • one year ago
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    Correct. We have one more step. We still need to deal with the fractional exponent.

  21. mathstudent55
    • one year ago
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    Here is the rule for a fractional exponent with numerator 1: \(\Large a^{\frac{1}{n}} = \sqrt[n]{a} \)

  22. mathstudent55
    • one year ago
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    A fractional exponent is a root. The denominator tells you which root it is.

  23. mathstudent55
    • one year ago
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    |dw:1434408876045:dw|

  24. anonymous
    • one year ago
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    I see. I see

  25. mathstudent55
    • one year ago
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    That is the final answer. Here are all the steps in one single drawing: |dw:1434408951600:dw|

  26. anonymous
    • one year ago
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    what happened to the 1/2?

  27. anonymous
    • one year ago
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    @mathstudent55 sorry :) I'm just curious!

  28. anonymous
    • one year ago
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    @mathstudent55 Is there a certain rule for this up above?

  29. anonymous
    • one year ago
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    @mathstudent55 please helppp

  30. mathstudent55
    • one year ago
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    @JasperRayWolf-Alysa88 We used two rules that I wrote above: \(\large a^{-n} = \dfrac{1}{a^n} \) \(\large a^{\frac{1}{n}} = \sqrt[n] a\)

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