The user has provided a series of mathematical expressions without a specific question. I will interpret these as individual problems to be solved or simplified.

Решение:

1. \(\frac{27}{15} \cdot \frac{125}{81} = \frac{3 \cdot 9}{3 \cdot 5} \cdot \frac{5 \cdot 25}{9 \cdot 9} = \frac{3}{5} \cdot \frac{25}{9} = \frac{3 \cdot 5 \cdot 5}{5 \cdot 3 \cdot 3} = \frac{5}{3}\)
2. \(\frac{49}{144} \cdot \frac{36}{245} = \frac{7 \cdot 7}{4 \cdot 36} \cdot \frac{36}{5 \cdot 49} = \frac{7 \cdot 7}{4 \cdot 36} \cdot \frac{36}{5 \cdot 7 \cdot 7} = \frac{1}{4} \cdot \frac{1}{5} = \frac{1}{20}\)
3. \(0.63 : 0.25 = \frac{63}{100} : \frac{25}{100} = \frac{63}{100} \cdot \frac{100}{25} = \frac{63}{25} = 2.52\)
4. \(0.8 : \frac{1}{125} = \frac{8}{10} : \frac{1}{125} = \frac{4}{5} \cdot 125 = \frac{4 \cdot 125}{5} = 4 \cdot 25 = 100\)
5. \(\frac{4}{4} : \frac{27}{49} = 1 : \frac{27}{49} = 1 \cdot \frac{49}{27} = \frac{49}{27}\)
6. \(\frac{16}{48} \cdot 3 = \frac{1}{3} \cdot 3 = 1\)
7. \(\frac{27}{3^2 \cdot 2^2} = \frac{3^3}{3^2 \cdot 2^2} = \frac{3}{2^2} = \frac{3}{4}\)
8. \(\frac{48}{24 \cdot 3} = \frac{48}{72} = \frac{2 \cdot 24}{3 \cdot 24} = \frac{2}{3}\)
9. \(\frac{3^{-6} \cdot 3^{17}}{27^4} = \frac{3^{-6+17}}{(3^3)^4} = \frac{3^{11}}{3^{12}} = 3^{11-12} = 3^{-1} = \frac{1}{3}\)

Ответ: \(\frac{5}{3}\), \(\frac{1}{20}\), \(2.52\), \(100\), \(\frac{49}{27}\), \(1\), \(\frac{3}{4}\), \(\frac{2}{3}\), \(\frac{1}{3}\).