Difference between revisions of "1993 AHSME Problems/Problem 3"
(Created page with "== Problem == <math>\frac{15^{30}}{45^{15}} =</math> <math>\text{(A)} \left(\frac{1}{3}\right)^{15}\quad \text{(B)} \left(\frac{1}{3}\right)^{2}\quad \text{(C)} 1\quad \text{(D)...") |
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<math>\frac{15^{30}}{45^{15}} =</math> | <math>\frac{15^{30}}{45^{15}} =</math> | ||
| − | <math>\text{(A)} \left(\frac{1}{3}\right)^{15}\quad | + | <math>\text{(A) } \left(\frac{1}{3}\right)^{15}\quad |
| − | \text{(B)} \left(\frac{1}{3}\right)^{2}\quad | + | \text{(B) } \left(\frac{1}{3}\right)^{2}\quad |
| − | \text{(C)} 1\quad | + | \text{(C) } 1\quad |
| − | \text{(D)} 3^{15}\quad | + | \text{(D) } 3^{15}\quad |
| − | \text{(E)} 5^{15}</math> | + | \text{(E) } 5^{15}</math> |
== Solution == | == Solution == | ||
| + | |||
| + | 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 | ||
| + | |||
| + | <math>\frac{15^{30}}{15^{15} \cdot 3^{15}}</math> | ||
| + | |||
| + | Canceling.... | ||
| + | |||
| + | <math>\frac{15^{15}}{3^{15}} \Rightarrow (\frac{15}{3})^{15} \Rightarrow 5^{15}</math> | ||
| + | |||
<math>\fbox{E}</math> | <math>\fbox{E}</math> | ||
Latest revision as of 23:34, 29 November 2016
Problem
Solution
First we must convert these to the same bases. We can rewrite 
as 
Now
Canceling....
See also
| 1993 AHSME (Problems • Answer Key • Resources) | ||
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
