# 1992 AHSME Problems/Problem 6

## Problem

If $x>y>0$ , then $\frac{x^y y^x}{y^y x^x}=$ $\text{(A) } (x-y)^{y/x}\quad \text{(B) } \left(\frac{x}{y}\right)^{x-y}\quad \text{(C) } 1\quad \text{(D) } \left(\frac{x}{y}\right)^{y-x}\quad \text{(E) } (x-y)^{x/y}$

## Solution

We see that this fraction can easily be factored as $\frac{x^y}{y^y}\times\frac{y^x}{x^x}$. Since $\frac{y^x}{x^x}=\frac{x^{-x}}{y^{-x}}$, this fraction is equivalent to $\left(\frac{x}{y}\right)^y\times\left(\frac{x}{y}\right)^{-x}=\left(\frac{x}{y}\right)^{y-x}\quad$, which corresponds to answer choice $\fbox{D}$.

## See also

 1992 AHSME (Problems • Answer Key • Resources) Preceded byProblem 5 Followed byProblem 7 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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