Difference between revisions of "1993 AHSME Problems/Problem 3"

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== Solution ==
 
== Solution ==
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First we must convert these to the same bases. We can rewrite <math>45^{15}</math> as <math>15^{15} \cdot 3^{15}</math> Now
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<math>\frac{15^{30}}{15^{15} \cdot 3^{15}}</math>
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Canceling....
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<math>\frac{15^{15}}{3^{15}} \Rightarrow (\frac{15}{3})^{15} \Rightarrow 5^{15}</math>
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<math>\fbox{E}</math>
 
<math>\fbox{E}</math>
  

Latest revision as of 00:34, 30 November 2016

Problem

$\frac{15^{30}}{45^{15}} =$

$\text{(A) } \left(\frac{1}{3}\right)^{15}\quad \text{(B) } \left(\frac{1}{3}\right)^{2}\quad \text{(C) } 1\quad \text{(D) } 3^{15}\quad \text{(E) } 5^{15}$

Solution

First we must convert these to the same bases. We can rewrite $45^{15}$ as $15^{15} \cdot 3^{15}$ Now

$\frac{15^{30}}{15^{15} \cdot 3^{15}}$

Canceling....

$\frac{15^{15}}{3^{15}} \Rightarrow (\frac{15}{3})^{15} \Rightarrow 5^{15}$

$\fbox{E}$

See also

1993 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 2
Followed by
Problem 4
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 26 27 28 29 30
All AHSME Problems and Solutions

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