2010 AMC 8 Problems/Problem 24
Problem
What is the correct ordering of the three numbers, , , and ?
$\textbf{(A)}\ 2^2^4<10^8<5^1^2$ (Error compiling LaTeX. ! Double superscript.) $\textbf{(B)}\ 2^2^4<5^1^2<10^8$ (Error compiling LaTeX. ! Double superscript.) $\textbf{(C)}\ 5^1^2<2^2^4<10^8$ (Error compiling LaTeX. ! Double superscript.) $\textbf{(D)}\ 10^8<5^1^2<2^2^4$ (Error compiling LaTeX. ! Double superscript.) $\textbf{(E)}\ 10^8<2^2^4<5^1^2$ (Error compiling LaTeX. ! Double superscript.)
Solution
Since all of the exponents are multiples of four, we can simplify the problem by taking the fourth root of each number. Evaluating we get , , and . Since , it follows that $\boxed{\textbf{(A)}\ 2^2^4<10^8<5^1^2 }$ (Error compiling LaTeX. ! Double superscript.) is the correct answer.
See Also
2010 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 23 |
Followed by Problem 25 | |
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All AJHSME/AMC 8 Problems and Solutions |