\[\left( 1\frac{11}{13} \right)^{12}:\left( 1\frac{11}{13} \right)^{16} \cdot 1\frac{11}{13} =\]
\[= \left( \frac{24}{13} \right)^{2} = \frac{576}{169} = 3\frac{69}{169}\]