2014 AMC 10B Problems/Problem 2

Problem

What is $\frac{2^3 + 2^3}{2^{-3} + 2^{-3}}$ ?

$\textbf {(A) } 16 \qquad \textbf {(B) } 24 \qquad \textbf {(C) } 32 \qquad \textbf {(D) } 48 \qquad \textbf {(E) } 64$

We can synchronously multiply ${2^3}$ to the polynomials both above and below the fraction bar. Thus, $\frac{2^3+2^3}{2^{-3}+2^{-3}}$

\[implies \=\frac{2^6+2^6}{1+1}={2^6}\] (Error compiling LaTeX. Unknown error_msg)

, which can be calculated resulting in 64. Therefore, the fraction equals to $\boxed{{64 (\textbf{E})}}$ .

2014 AMC 10B (Problems • Answer Key • Resources)
Preceded by Problem 1	Followed by Problem 3
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