e) \(\dfrac{\left(\dfrac{2}{3}\right)^3\left(-\dfrac{3}{4}\right)^2\left(-1\right)^5}{\left(\dfrac{2}{5}\right)^2\left(-\dfrac{5}{12}\right)^3}\)
\(=\dfrac{\dfrac{8}{27}.\dfrac{9}{16}.\left(-1\right)}{\dfrac{4}{25}.\left(-\dfrac{125}{1728}\right)}\)
\(=\dfrac{-\dfrac{1}{6}}{-\dfrac{5}{432}}\)
=\(\dfrac{72}{5}\)
Ta có: \(\dfrac{\left(\dfrac{2}{3}\right)^7\cdot\left(-\dfrac{3}{4}\right)^2\cdot\left(-1\right)^5}{\left(\dfrac{2}{5}\right)^2\cdot\left(-\dfrac{5}{12}\right)^3}\)
\(=\dfrac{\dfrac{2^7}{3^7}\cdot\dfrac{3^2}{4^2}\cdot\left(-1\right)}{\dfrac{2^2}{5^2}\cdot\dfrac{5^3}{-2^6\cdot3^3}}\)
\(=\dfrac{\dfrac{2^7}{3^5\cdot2^4}\cdot\left(-1\right)}{\dfrac{5}{-2^4\cdot3^3}}\)
\(=\dfrac{-8}{3^5}\cdot\dfrac{-2^4\cdot3^3}{5}\)
\(=\dfrac{72}{5}\)
