\(-\dfrac{1}{9}:\dfrac{13}{8}+\left(-\dfrac{1}{9}\right):\dfrac{13}{5}+\left(-\dfrac{2}{3}\right)^2\)
\(=\left(-\dfrac{1}{9}\right)\times\dfrac{8}{13}+\left(-\dfrac{1}{9}\right)\times\dfrac{5}{13}+\dfrac{4}{9}\)
\(=\left(-\dfrac{1}{9}\right)\left(\dfrac{8}{13}+\dfrac{5}{13}\right)+\dfrac{4}{9}\)
\(=\left(-\dfrac{1}{9}\right)\cdot1+\dfrac{4}{9}\)
\(=\left(-\dfrac{1}{9}\right)+\dfrac{4}{9}\)
\(=\dfrac{3}{9}=\dfrac{1}{3}\)