# 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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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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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.

Colby

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.