Difference between revisions of "2002 AMC 10P Problems/Problem 1"

(Solution 1)
(Solution 1)
 
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We can use basic rules of exponentiation to solve this problem.
 
We can use basic rules of exponentiation to solve this problem.
  
\begin{align*}
+
<math>\frac{(2^4)^8}{(4^8)^2}  
\frac{(2^4)^8}{(4^8)^2} \\
+
=\frac{(2^4)^8}{(2^{16})^2}  
=\frac{(2^4)^8}{(2^16)^2} \\
+
=\frac{2^{32}}{2^{32}}
=\frac{2^32}{2^32} \\
+
=1</math>
=1 \\
 
\end{align*}
 
  
 
Thus, our answer is <math>\boxed{\textbf{(C) } 1}.</math>
 
Thus, our answer is <math>\boxed{\textbf{(C) } 1}.</math>

Latest revision as of 19:16, 14 July 2024

Problem

The ratio $\frac{(2^4)^8}{(4^8)^2}$ equals

$\text{(A) }\frac{1}{4} \qquad \text{(B) }\frac{1}{2} \qquad \text{(C) }1 \qquad \text{(D) }2 \qquad \text{(E) }8$

Solution 1

We can use basic rules of exponentiation to solve this problem.

$\frac{(2^4)^8}{(4^8)^2}  =\frac{(2^4)^8}{(2^{16})^2}  =\frac{2^{32}}{2^{32}}  =1$

Thus, our answer is $\boxed{\textbf{(C) } 1}.$

See also

2002 AMC 10P (ProblemsAnswer KeyResources)
Preceded by
First question
Followed by
Problem 2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 10 Problems and Solutions

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