\(\dfrac{-1}{9}:\dfrac{13}{8}+\dfrac{-1}{9}:\dfrac{13}{5}+\left(-\dfrac{2}{3}\right)^2\)
\(=\dfrac{-1}{9}\cdot\dfrac{8}{13}+\dfrac{-1}{9}\cdot\dfrac{5}{13}+\dfrac{4}{9}\)
\(=-\dfrac{1}{9}\left(\dfrac{8}{13}+\dfrac{5}{13}\right)+\dfrac{4}{9}=\dfrac{4}{9}-\dfrac{1}{9}=\dfrac{3}{9}=\dfrac{1}{3}\)