Difference between revisions of "2013 AMC 10A Problems/Problem 8"

Revision as of 21:58, 7 February 2013

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

$\textbf{(A)}\ -1 \qquad\textbf{(B)}\ 1 \qquad\textbf{(C)}\ \frac{5}{3} \qquad\textbf{(D)}\ 2013 \qquad\textbf{(E)}\ 2^{4024}$

Factoring out, we get: $\frac{2^{2012}(2^2 + 1)}{2^{2012}(2^2-1)} ?$

Cancelling out the $2^{2012}$ from the numerator and denominator, we see that it simplifies to $\frac{5}{3}$ , $\textbf{(C)}$ .

2013 AMC 10A (Problems • Answer Key • Resources)
Preceded by Problem 7	Followed by Problem 9
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AMC 10 Problems and Solutions

2013 AMC 12A (Problems • Answer Key • Resources)
Preceded by Problem 3	Followed by Problem 5
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AMC 12 Problems and Solutions

@@ Line 16: / Line 16: @@
 Cancelling out the <math>2^{2012}</math> from the numerator and denominator, we see that it simplifies to <math>\frac{5}{3}</math>, <math>\textbf{(C)}</math>.
+==See Also==
+{{AMC10 box|year=2013|ab=A|num-b=7|num-a=9}}
+{{AMC12 box|year=2013|ab=A|num-b=3|num-a=5}}