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2013 AMC 12A Problem 4

Problem 4 of 25EasierAlgebra

What is the value of 22014+2201222014−22012?\dfrac{2^{2014} + 2^{2012}}{2^{2014} - 2^{2012}}?

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Solution

Factoring 220122^{2012} from each term gives 22012(22+1)22012(22−1)=4+14−1=53. \dfrac{2^{2012}(2^2 + 1)}{2^{2012}(2^2 - 1)} = \dfrac{4 + 1}{4 - 1} = \dfrac{5}{3}. Thus, the correct answer is C.

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Concepts: exponent · factoring

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