2010 AMC8 Problem 24

#1
What is the correct ordering of the three numbers, \(10^8\), \(5^{12}\), and \(2^{24}\)?

\( \textbf{(A)}\ 2{}^2{}^4<10^8<5{}^1{}^2 \)

\( \textbf{(B)}\ 2{}^2{}^4<5{}^1{}^2<10^8 \)

\( \textbf{(C)}\ 5{}^1{}^2<2{}^2{}^4<10^8 \)

\( \textbf{(D)}\ 10^8<5{}^1{}^2<2{}^2{}^4\)

\( \textbf{(E)}\ 10^8<2{}^2{}^4<5{}^1{}^2 \)