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'Giants' printed from http://nrich.maths.org/
Which is bigger: $9^{10}$ or $10^{9}$?
Now find a way to use your calculator to compare $99^{100}$ and
$100^{99}$.
Work out which is bigger out of $999^{1000}$ and
$1000^{999}$.
NOTES AND BACKGROUND
This challenge calls for some experimentation with numbers and for
some ingenuity in finding a solution. There are several possible
methods of solution.
Optional extension challenge: If
you solved the above, you might wish to consider which is bigger
for the same sort of problem with a billion 9s and a billion
0s.