a) \(\left(\dfrac{5}{2}\right)^3.\left(\dfrac{4}{5}\right)^3=\dfrac{5^3}{2^3}.\dfrac{4^3}{5^3}\) \(=\dfrac{5^3}{2^3}.\dfrac{\left(2^3\right)^3}{5^3}=2^3=8\)
b) \(\left(\dfrac{1}{9}\right)^2:\left(\dfrac{1}{3}\right)^3=\dfrac{1}{9^2}:\dfrac{1}{3^3}=\dfrac{1}{\left(3^2\right)^2}.3^3=\dfrac{3^3}{3^4}=\dfrac{1}{3}\)
c) \(\left(\dfrac{9}{5}\right)^5:\left(\dfrac{27}{-20}\right)^5=\dfrac{9^5}{5^5}:\dfrac{27^5}{\left(-20\right)^5}=\dfrac{\left(3^2\right)^5}{5^5}.\dfrac{\left(-4.5\right)^5}{\left(3^3\right)^5}\)
\(=-\dfrac{3^{10}}{5^5}.\dfrac{4^5.5^5}{3^{15}}=-\dfrac{4^5}{3^5}=\dfrac{-1024}{243}\)
d) \(3^3.9^{-1}=3^3.\dfrac{1}{9}=\dfrac{3^3}{3^2}=3\)
