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AngelaB97

  • one year ago

can someone please help me understand radicals??

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  1. AngelaB97
    • one year ago
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    |dw:1441684069299:dw|

  2. AngelaB97
    • one year ago
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    how would you solve this?

  3. AngelaB97
    • one year ago
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    @Jhannybean

  4. Jhannybean
    • one year ago
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    \[\large \sqrt[5]{\frac{1}{8}} \cdot \sqrt[5]{\frac{1}{4}}\]

  5. Jhannybean
    • one year ago
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    Let's start by rewriting this as a fraction with a power. Recall that \(\large \sqrt[n]{x^m} =(x^m)^n\)\[\left(\frac{1}{8}\right)^{1/5}\]Can you tellme how we would write the other fraction?

  6. AngelaB97
    • one year ago
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    (1/4) ^1/5

  7. Jhannybean
    • one year ago
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    Awesome. Now we multiply them together. \[\left(\frac{1}{8}\right)^{1/5}\cdot \left(\frac{1}{4}\right)^{1/5}\] Next we distribute the fractional power to all terms within the parenthesis \[\left(\frac{1}{8^{1/5}}\right)\left(\frac{1}{4^{1/5}}\right)\]

  8. Jhannybean
    • one year ago
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    And now we just multiply.

  9. Jhannybean
    • one year ago
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    \[\frac{1}{8^{1/5} \cdot 4^{1/5}} = \frac{1}{32^{1/5}} \]

  10. Jhannybean
    • one year ago
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    Now an easy way to think about it is finding the prime factors of 32. What are they?

  11. AngelaB97
    • one year ago
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    8 and 4?

  12. Jhannybean
    • one year ago
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    Yes, and if we break 8 and 4 down even further, what would we get?

  13. AngelaB97
    • one year ago
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    |dw:1441685366603:dw|

  14. Jhannybean
    • one year ago
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    Is that a question mark?

  15. Jhannybean
    • one year ago
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    |dw:1441685422951:dw|

  16. AngelaB97
    • one year ago
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    question mark lol

  17. Jhannybean
    • one year ago
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    Ok haha.

  18. Jhannybean
    • one year ago
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    You're right about the 2, Now let's break 32 apart. \[(32)^{1/5} = (2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2)^{1/5}\] The \(\frac{1}{5}\) power represents the 5th root. This means that for every PAIR of FIVE numbers, 1 will come out of the 5th root. Therefore since there are exactly five 2's under the 5th root, we are going to only use one 2.

  19. Jhannybean
    • one year ago
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    Does that make sense, @AngelaB97 ?

  20. Jhannybean
    • one year ago
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    Therefore \(\dfrac{1}{32^{1/5}} = \boxed{\dfrac{1}{2}}\)

  21. AngelaB97
    • one year ago
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    yes thanks so much once again @Jhannybean

  22. AngelaB97
    • one year ago
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    sorry to bother you again

  23. Jhannybean
    • one year ago
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    No problem :)

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