17^3 • 18^9 : 18^4 • 17^5

To simplify the expression \( \frac{17^3 \cdot 18^9}{18^4 \cdot 17^5} \), we can break it down as follows:

1. Separate the fractions: \[ \frac{17^3}{17^5} \cdot \frac{18^9}{18^4} \]

2. Apply the property of exponents \( \frac{a^m}{a^n} = a^{m-n} \): \[ 17^{3-5} \cdot 18^{9-4} \]

3. Calculate the exponents: \[ 17^{-2} \cdot 18^{5} \]

4. Rewrite \( 17^{-2} \) as \( \frac{1}{17^2} \): \[ \frac{18^5}{17^2} \]

So, the simplified expression is: \[ \frac{18^5}{17^2} \]