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Johan14th

  • one year ago

can someone help me find the power form of the reciprocal radical form 1/(3 sqrt.three(x^2))

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  1. Johan14th
    • one year ago
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    \[\frac{ 1 }{ 3\sqrt[3]{x ^{2}}}\]

  2. anonymous
    • one year ago
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    you have a simple formula for radicals \[\sqrt[a]{x^b}=x^\frac{b}{a}\]|dw:1444074783490:dw|

  3. anonymous
    • one year ago
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    Also \[x^n=\frac{1}{x^{-n}} \space \space \space ; \space \space \space \frac{1}{x^n}=x^{-n}\] Just add a minus sign to the exponent when u move the number from numerator to denominator or vice versa

  4. anonymous
    • one year ago
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    |dw:1444075056599:dw|

  5. anonymous
    • one year ago
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    @Johan14th r u there?

  6. Johan14th
    • one year ago
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    yes so then it would be x^ 2/3

  7. Johan14th
    • one year ago
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    \[3x^{\frac{ 2 }{ 3 }}\]

  8. anonymous
    • one year ago
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    no! you're not done yet!!

  9. anonymous
    • one year ago
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    \[\frac{1}{3x^{\frac{2}{3}}}\]

  10. anonymous
    • one year ago
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    We need to bring the number to the top now!! |dw:1444075590776:dw|

  11. Johan14th
    • one year ago
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    oh okay so then it is \[3x^{\frac{- 3 }{ 2 }}\]

  12. Johan14th
    • one year ago
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    and then i could apply the power rule right?

  13. anonymous
    • one year ago
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    Hmm, you only change the sign, you leave the fraction unchanged, also the number 3 will stay in the bottom, if you want to bring the 3 to the top, you must write -1 to it's power \[\frac{1}{3x^{\frac{2}{3}}}=\frac{x^{-\frac{2}{3}}}{3}=3^{-1}x^{-\frac{2}{3}}\]

  14. Johan14th
    • one year ago
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    okay so basically adding the (-) to the power makes it go on to the top of the fraction, numerator. if i want to do the same to the 3 (too get rid of the fraction) i add the (-) to the power

  15. anonymous
    • one year ago
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    Yes, anytime you bring a number or letter from top to bottom, or from bottom to top, you change the sign of it's power, very important, remember this rule

  16. anonymous
    • one year ago
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    for example if we had \[\frac{1}{3^{-1}}\] If we bring it to the top it becomes \[\frac{1}{3^{-1}}=3^{1}=3\]

  17. Johan14th
    • one year ago
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    okay that just cleared everything out. thank you. i was trying too do some weird multiplication. you saved me!

  18. anonymous
    • one year ago
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    you're absolutely welcome

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