What is the correct ordering of the three numbers, $10^8$, $5^{12}$, and $2^{24}$?
$\textbf{(A)}\ 2^{24}<10^8<5^{12}\\ \textbf{(B)}\ 2^{24}<5^{12}<10^8 \\  \textbf{(C)}\ 5^{12}<2^{24}<10^8 \\ \textbf{(D)}\ 10^8<5^{12}<2^{24} \\ \textbf{(E)}\ 10^8<2^{24}<5^{12}$
Use brute force.
$10^8=100,000,000$, 
$5^{12}=244,140,625$, and
$2^{24}=16,777,216$.
Therefore, $\boxed{\text{(A)}2^{24}<10^8<5^{12}}$ is the answer. (Not recommended for the contest and will take forever)