questionnaire

03-04-2015, 06:35 PM

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 ).

YaSvoboden

03-11-2015, 05:50 PM

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 < (2^8)^2000= 2^16000, so it is less than c and d.

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.