anonymous
  • anonymous
how do i simplify nested roots and powers of a single positive variable?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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TuringTest
  • TuringTest
\[\large (x^a)^b=x^{ab}\]
TuringTest
  • TuringTest
\[\sqrt[b]{x^a}=x^{a/b}\]so those can be used together
anonymous
  • anonymous
how would i solve this type of problem then?|dw:1328571176207:dw|

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anonymous
  • anonymous
raise the equation to the power if 6 then simplify, then take it to the 1/6
anonymous
  • anonymous
how'd u get that... if you don't mind.
anonymous
  • anonymous
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
anonymous
  • anonymous
|dw:1328571786972:dw| lol. is this what you do though? I know i got a different answer...
TuringTest
  • TuringTest
I can't see the whole problem, is it an equation or simplification?
anonymous
  • anonymous
simplify
TuringTest
  • TuringTest
\[\sqrt{x\sqrt[3]{x^2}}\]is all I can see, is there more?
anonymous
  • anonymous
no lol, that was it
anonymous
  • anonymous
use the first power rule given by turing test
anonymous
  • anonymous
i dont understand why i would use the first one and not the second
TuringTest
  • TuringTest
\[\large\sqrt{x\sqrt[3]{x^2}}=(x\cdot x^{3/2})^{1/2}=x^{1/2}\cdot x^{(3/2)\cdot(1/2)}\]simplify the fractions
anonymous
  • anonymous
same principal different ways of represent the function
anonymous
  • anonymous
|dw:1328572233670:dw|
TuringTest
  • TuringTest
we use four rules here really:\[\sqrt[b]{x^a}=x^{a/b}\]\[(xy)^a=x^ay^a\]\[(x^a)^b=x^{ab}\]\[x^ax^b=x^{a+b}\]\[\large\sqrt{x\sqrt[3]{x^2}}=(x\cdot x^{3/2})^{1/2}=x^{1/2}\cdot x^{(3/2)\cdot(1/2)}\]
TuringTest
  • TuringTest
or if you prefer\[\large\sqrt{x\sqrt[3]{x^2}}=(x\cdot x^{\frac32})^{\frac12}=(x^{1+\frac32})^{\frac12}=x^{(\frac52\cdot\frac12)}=x^{\frac54}\]
anonymous
  • anonymous
gotttttttt it. ty test
TuringTest
  • TuringTest
welcome :D

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