Which has greater value?

$2^8=256$ $2^{1000}=\left(2^8 \right)^{125}=256^{125}>255^{125}$

Let 2 $^{1000}$ =x

Then

log2 $^{1000}$ =logx

1000log 2=log x

301.03=log x

10 $^{301.03}$ =x

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Let 255 $^{125}$ =y

Then

log 255 $^{125}$ =log y

125log 255=log y

300.8125=log y

10 $^{300.8125}$ =y

So 2 $^{1000}$ >255 $^{125}$

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I know this solution is harder than that of @BLCRAFT Gaming , but it can be basis of many questions of this type

$2^{1000} = (2^{8})^{125}$

$255^{125} = (256 - 1)^{125} = (2^8 - 1)^{125}$

Furthermore:

$2^8 > (2^8 - 1)$

i.e.

$2^{1000} > 255^{125}$