# Which is bigger: # ( 1 + \sqrt{2} )^{ 1 + \sqrt{2} + 10^{-9,000} } # or # ( 1 + \sqrt{2} + 10^{-9,000} )^{ 1 + \sqrt{2} } # ? If your calculator could actually handle this -- please put it away !! :)

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(I have hints available, if necessary.)

(I have hints available, if necessary.)

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See below.

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Calling

both

and

now

and consequently

but

Considering now that

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#### Answer:

I think both are equal.

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#10^-9000->0# as its value is negligible.Then

#(1+sqrt2)^(1+sqrt2+0)=(1+sqrt2+0)^(1+sqrt2)# .Otherwise, I was thinking about logarithm concept.

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