questionnaire Posted March 4, 2015 Share Posted March 4, 2015 Which one of the the following numbers is the largest? A) 200^2000. B) 9^5120. C) 2^2^14. D) (64000)*(64001)*(64002)*(64003)*(64004)*...*(65000). Quote Link to comment Share on other sites More sharing options...
YaSvoboden Posted March 11, 2015 Share Posted March 11, 2015 Fun question. I am pretty sure that the answer is B) c) is 2^16284 d) 64000 is pretty close to 2^16. This is basically (2^16)^1000, or pretty close to c at 2^16000 a) 200 is less than 256. so 200^2000 b) This is a little trickier to think of because it is tougher to break into a comparable form. But 9^5160 = (3^3)^5160=3^15480. It seems like that base 3 would be enough to overcome the difference in exponents. To verify, 3>2^(3/2), so 3^15480>(2^(3/2))^15480=2^23220. So yeah, it looks like b is the biggest. Quote Link to comment Share on other sites More sharing options...
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