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

(Solution 1)
(Solution 1)
Line 23: Line 23:
 
<math>=\frac{2^32}{2^32}</math>
 
<math>=\frac{2^32}{2^32}</math>
  
<math>=</math>1<math>
+
<math>=1</math>
  
Thus, our answer is </math>\boxed{\textbf{(C) } 1}.$
+
Thus, our answer is <math>\boxed{\textbf{(C) } 1}.</math>
  
 
== See also ==
 
== See also ==
 
{{AMC10 box|year=2002|ab=P|before=First question|num-a=2}}
 
{{AMC10 box|year=2002|ab=P|before=First question|num-a=2}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 18:11, 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.

$\frac{(2^4)^8}{(4^8)^2}$

$=\frac{(2^4)^8}{2^16}^2}$ (Error compiling LaTeX. Unknown error_msg)

$=\frac{2^32}{2^32}$

$=1$

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

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png