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.