\(\left(\dfrac{1}{3}\right)^{50}.\left(-9\right)^{25}-\dfrac{2}{3}:4\)
\(=\left(\dfrac{1}{3}\right)^{50}.\left[\left(-3\right)^2\right]^{25}-\dfrac{2}{3}.\dfrac{1}{4}\)
\(=\left(\dfrac{1}{3}\right)^{50}.\left(-3\right)^{50}-\dfrac{2}{12}\)
\(=\left[\dfrac{1}{3}.\left(-3\right)\right]^{50}-\dfrac{1}{6}\)
\(=\left(-1\right)^{50}-\dfrac{1}{6}\)
\(=1-\dfrac{1}{6}\)
\(=\dfrac{6}{6}-\dfrac{1}{6}\)
\(=\dfrac{5}{6}\)
\(\left(\dfrac{1}{3}\right)^{50}\cdot\left(-9\right)^{25}-\dfrac{2}{3}:4=\)
=\(\dfrac{1}{3^{50}}\cdot\left(-9\right)^{25}-\dfrac{2}{3}\cdot\dfrac{1}{4}\)
=\(\dfrac{\left(-9\right)^{25}}{9^{25}}-\dfrac{1}{6}\)
=\(-1-\dfrac{1}{6}\)
=\(-\dfrac{6}{6}-\dfrac{1}{6}\)
=\(-\dfrac{7}{6}\)
