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2013 AMC 10A Problem 8

Problem 8 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 out a 22012,2^{2012}, we get: 22012(22+1)22012(22−1)=53. \dfrac{2^{2012}(2^2 + 1)}{2^{2012}(2^2 - 1)} = \dfrac{5}{3}. Thus, C is the correct answer.

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Concepts: exponent · factoring

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