4.10. \(\dfrac{18^4\cdot10^2}{15^3\cdot12^5}\)

Разложим основания: \(18=2\cdot3^2\), \(10=2\cdot5\), \(15=3\cdot5\), \(12=2^2\cdot3\).

\(\dfrac{18^4\cdot10^2}{15^3\cdot12^5}=\dfrac{2^6\cdot3^8\cdot5^2}{2^{10}\cdot3^8\cdot5^3}=\dfrac{1}{2^4\cdot5}=\dfrac{1}{80}\).

Ответ: \(\dfrac{1}{80}\).