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anonymous

  • 4 years ago

how do i simplify nested roots and powers of a single positive variable?

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  1. TuringTest
    • 4 years ago
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    \[\large (x^a)^b=x^{ab}\]

  2. TuringTest
    • 4 years ago
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    \[\sqrt[b]{x^a}=x^{a/b}\]so those can be used together

  3. anonymous
    • 4 years ago
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    how would i solve this type of problem then?|dw:1328571176207:dw|

  4. anonymous
    • 4 years ago
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    raise the equation to the power if 6 then simplify, then take it to the 1/6

  5. anonymous
    • 4 years ago
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    how'd u get that... if you don't mind.

  6. anonymous
    • 4 years ago
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    got rid of the radicals, using the power rules. easily all you have to do is take the product of each of the nested radicals. make sure you dont forget to apply the power non nested equation. this was simple equation when you get (x +2 + (x)^1/2))^1/2 it becomes very difficult

  7. anonymous
    • 4 years ago
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    |dw:1328571786972:dw| lol. is this what you do though? I know i got a different answer...

  8. TuringTest
    • 4 years ago
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    I can't see the whole problem, is it an equation or simplification?

  9. anonymous
    • 4 years ago
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    simplify

  10. TuringTest
    • 4 years ago
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    \[\sqrt{x\sqrt[3]{x^2}}\]is all I can see, is there more?

  11. anonymous
    • 4 years ago
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    no lol, that was it

  12. anonymous
    • 4 years ago
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    use the first power rule given by turing test

  13. anonymous
    • 4 years ago
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    i dont understand why i would use the first one and not the second

  14. TuringTest
    • 4 years ago
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    \[\large\sqrt{x\sqrt[3]{x^2}}=(x\cdot x^{3/2})^{1/2}=x^{1/2}\cdot x^{(3/2)\cdot(1/2)}\]simplify the fractions

  15. anonymous
    • 4 years ago
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    same principal different ways of represent the function

  16. anonymous
    • 4 years ago
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    |dw:1328572233670:dw|

  17. TuringTest
    • 4 years ago
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    we use four rules here really:\[\sqrt[b]{x^a}=x^{a/b}\]\[(xy)^a=x^ay^a\]\[(x^a)^b=x^{ab}\]\[x^ax^b=x^{a+b}\]\[\large\sqrt{x\sqrt[3]{x^2}}=(x\cdot x^{3/2})^{1/2}=x^{1/2}\cdot x^{(3/2)\cdot(1/2)}\]

  18. TuringTest
    • 4 years ago
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    or if you prefer\[\large\sqrt{x\sqrt[3]{x^2}}=(x\cdot x^{\frac32})^{\frac12}=(x^{1+\frac32})^{\frac12}=x^{(\frac52\cdot\frac12)}=x^{\frac54}\]

  19. anonymous
    • 4 years ago
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    gotttttttt it. ty test

  20. TuringTest
    • 4 years ago
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    welcome :D

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