During AMC testing, the AoPS Wiki is in read-only mode. No edits can be made.

1993 AHSME Problems/Problem 3

Revision as of 23:34, 29 November 2016 by Shootingstar8 (talk | contribs) (Solution)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

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

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

Invalid username
Login to AoPS