a, \(\left[6.\left(-\dfrac{1}{3}\right)^2-3\left(-\dfrac{1}{3}\right)+1\right]:\left(-\dfrac{1}{3}-1\right)\)
\(=\left[6.\dfrac{1}{9}-\dfrac{1.\left(-1\right)}{1}+1\right]:\left(-\dfrac{1}{3}-\dfrac{3}{3}\right)\)
\(=\left[\dfrac{2.1}{3}-\left(-1\right)+1\right]:\left(\dfrac{-4}{3}\right)\)
\(=\left[\dfrac{2}{3}+1+1\right].\left(\dfrac{-3}{4}\right)\)
\(=\left[\dfrac{2}{3}+\dfrac{3}{3}+\dfrac{3}{3}\right].\left(\dfrac{-3}{4}\right)\)
\(=\dfrac{8}{3}.\left(\dfrac{-3}{4}\right)\)
\(=\dfrac{2.\left(-1\right)}{1.1}\)
\(=-2\)
b: \(\dfrac{\left(\dfrac{2}{3}\right)^3\cdot\left(-\dfrac{3}{4}\right)^2\cdot\left(-1\right)^{2003}}{\left(\dfrac{2}{5}\right)^4\cdot\left(-\dfrac{5}{1}\right)^3}\)
\(=\dfrac{\dfrac{8}{27}\cdot\dfrac{9}{16}\cdot\left(-1\right)}{\dfrac{16}{625}\cdot\left(-125\right)}=\dfrac{\dfrac{1}{2}\cdot\dfrac{1}{3}\cdot\left(-1\right)}{-\dfrac{16}{5}}\)
\(=\dfrac{-1}{6}:\dfrac{-16}{5}=\dfrac{1}{6}\cdot\dfrac{5}{16}=\dfrac{5}{96}\)
