Ответ:

\(1\frac{7}{8}=\frac{15}{8}\), \(1\frac{1}{9}=\frac{10}{9}\), \(1\frac{23}{25}=\frac{48}{25}\).

\(\frac{15}{8}\cdot\frac{10}{9}\cdot\frac{48}{25}=\frac{3}{5}\cdot\frac{10}{9}\cdot6=\frac{3\cdot2\cdot6}{9}=4\).

Ответ: 4.