1993 AHSME Problems/Problem 3

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....

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

$\fbox{E}$

1993 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 2	Followed by Problem 4
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1993 AHSME Problems/Problem 3

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