2014 AMC 10B Problems/Problem 2

Problem

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

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

Solution

We can synchronously multiply ${2^3}$ to the polynomials both above and below the fraction bar. Thus,  (Error compiling LaTeX. ! Missing \$ inserted.)\frac{2^3+2^3}{2^{-3}+2^{-3}}=\frac{2^6+2^6}{1+1}={2^6},$resulting in 64.$$Therefore, the fraction equals to$\boxed{{64 (\textbf{E})}}.