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Answer: $3^{11} < 8^8  < 2^{25}$


We have $8^8= (2^3)^8=2^{24}=(2^2)^{12}=4^{12}> 3^{11}$
So $3^{11}< 8^8$
 
Also $2^{24}< 2^{25}$ so $8^8< 2^{25}$

So the order is $3^{11} < 8^8  < 2^{25}$
 
 
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.