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. Unknown error_msg) $\textbf{(B)}\ 2^2^4<5^1^2<10^8$ (Error compiling LaTeX. Unknown error_msg) $\textbf{(C)}\ 5^1^2<2^2^4<10^8$ (Error compiling LaTeX. Unknown error_msg) $\textbf{(D)}\ 10^8<5^1^2<2^2^4$ (Error compiling LaTeX. Unknown error_msg) $\textbf{(E)}\ 10^8<2^2^4<5^1^2$ (Error compiling LaTeX. Unknown error_msg)
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. Unknown error_msg) is the correct answer.
See Also
2011 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by First Problem |
Followed by Problem 2 | |
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All AJHSME/AMC 8 Problems and Solutions |