2013 AMC 10A Problem 8 — Solution | LIVE by Po-Shen Loh

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2013 AMC 10A Problem 8

Attempt Problem 8 of the 2013 AMC 10A below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2013 AMC 10A solutions, or check the answer key.

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8.

What is the value of $\dfrac{2^{2014}+2^{2012}}{2^{2014}-2^{2012}} ?$

$-1$

$1$

$\dfrac{5}{3}$

$2013$

$2^{4024}$

Answer: C

Concepts:exponent factoring

Difficulty rating: 870

Solution:

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.

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