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Thread: Difficult Math Question!

  1. #1
    Trying to make mom and pop proud
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    Difficult Math Question!

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    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 ).



  2. #2
    An Urch Guru Pundit Swami Sage
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    Re: Difficult Math Question!

    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.

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    Trying to make mom and pop proud cook90's Avatar
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    Re: Difficult Math Question!

    Hey, the correct answer is B
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