Problem 5 · 2014 Math Kangaroo
Easy
Algebra & Patterns
grouping
\(\dfrac{2^{2014}-2^{2013}}{2^{2013}-2^{2012}}={?}\)
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Answer: E — 2
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Hint 1 of 2
Factor the smallest power of 2 out of the top and out of the bottom.
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Hint 2 of 2
After factoring, almost everything cancels.
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Approach: factor common powers, then cancel
- Top: 2^{2014} − 2^{2013} = 2^{2013}(2 − 1) = 2^{2013}.
- Bottom: 2^{2013} − 2^{2012} = 2^{2012}(2 − 1) = 2^{2012}.
- Their ratio is 2^{2013}/2^{2012} = 2.
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