\(\left(\dfrac{1}{3}\right)^{50}.\left(-9\right)^{25}-\dfrac{2}{3}:4\)
\(=\left[\left(\dfrac{1}{3}\right)^2\right]^{25}.\left(-9\right)^{25}-\dfrac{1}{6}\)
\(=\left(\dfrac{1}{9}\right)^{25}.\left(-9\right)^{25}-\dfrac{1}{6}\)
\(=\left[\dfrac{1}{9}.\left(-9\right)\right]^{25}-\dfrac{1}{6}\)
\(=\left(-1\right)-\dfrac{1}{6}\)
\(=-\dfrac{7}{6}\)