The fraction $\frac{a^{-4}-b^{-4}}{a^{-2}-b^{-2}}$ is equal to: 
$\textbf{(A)}\ a^{-6}-b^{-6}\qquad\textbf{(B)}\ a^{-2}-b^{-2}\qquad\textbf{(C)}\ a^{-2}+b^{-2}\\ \textbf{(D)}\ a^2+b^2\qquad\textbf{(E)}\ a^2-b^2$
By the difference of squares property, $a^{-4} - b^{-4}$ is equivalent to $(a^{-2} + b^{-2})(a^{-2} - b^{-2})$. This means the fraction is now equal to $\frac{(a^{-2} + b^{-2})(a^{-2} - b^{-2})}{a^{-2} - b^{-2}}$, which simplifies to $\textbf{(C)}\ a^{-2}+b^{-2}$