What is the value of 2^2014+2^20122^2014-2^2012 ?

2013 AMC 10A Problem 8

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What is the value of

\dfrac{2^{2014}+2^{2012}}{2^{2014}-2^{2012}} ?

-1

1

\dfrac{5}{3}

2013

2^{4024}

Factor out the smaller power

2^{2012}

After factoring, only

2^2

remains in each parenthesis

Factoring out a

2^{2012},

we get:

\dfrac{2^{2012}(2^2 + 1)}{2^{2012}(2^2 - 1)} = \dfrac{5}{3}.

Thus, C is the correct answer.