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Please help me with this question: (x^x)^(x^-x) if x=-2   (x to the power of x)to the power of (x to the power of negative x)

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hala718 eNotes educator | Certified Educator

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We need to find the value of f(x) when x= -2

`f(x)= (x^x)^(x^-x)`

`==> f(-2)= (-2^-2)^(-2^2)`

`==> f(-2)= (-2^-2)^4`

`==> f(-2)= (-1/2^2)^4`

`==> f(-2)= (-1/4)^4`

`==> f(-2)= 1/4^4 = 1/256`

`==> `The value of `(x^x)^(x^-x)`  when x= -2 is `1/256`

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colbywaldorf55 | Student

i think the answer for f(-2)=-(1/64) as per my calculation. If the answer is not correct then please update it below and also the method by which you have solved it.


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disilvaalice | Student

Answer of your question is 1.41421356237

But this answer is calculated from the given form of question.(x^x)^(x^-x) if x=-2

Otherwise I'm agree with answer mentioed above.

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