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Power of exponents

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by rohu27 » Tue Mar 29, 2011 8:16 pm
A =1
B=2^300
D=2^200
E=2^200

dwn to B and C 2^300=(2^3)^100=8^100
3^200=9^100
so C>B
OA C
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by Anurag@Gurome » Tue Mar 29, 2011 8:19 pm
6983manish wrote:Which expression has the greatest value?

(A) 1^{999}
(B) 2^{300}
(C) 3^{200}
(D) 4^{100}
(E) 16^{50}
1^{999} = 1, which is the least value
4^{100} = 2^{200}
16^{50} = 2^{200}
So, choices (D) and (E) and the same and this value is less than 2^{300}. Only possibilities are (B) and (C).

2^{300} = (2^3)^100 = 8^100
3^{200} = (3^2)^100 = 9^100, which is the greatest value.

The correct answer is C.
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