a: \(\left(\dfrac{1}{2}\right)^5\cdot\left(\dfrac{1}{4}\right)^2=\left(\dfrac{1}{2}\right)^5\cdot\left(\dfrac{1}{2}\right)^4=\left(\dfrac{1}{2}\right)^9=\dfrac{1}{512}\)
b: \(\left(-\dfrac{1}{2}\right)^2\cdot\left(\dfrac{2}{5}\right)^2=\left(-\dfrac{1}{2}\cdot\dfrac{2}{5}\right)^2=\left(-\dfrac{1}{5}\right)^2=\dfrac{1}{25}\)
c: \(\left(-\dfrac{5}{4}\right)^2:\left(-\dfrac{35}{24}\right)^2=\left(\dfrac{5}{4}\right)^2:\left(\dfrac{35}{24}\right)^2\)
\(=\left(\dfrac{5}{4}:\dfrac{35}{24}\right)^2=\left(\dfrac{5}{4}\cdot\dfrac{24}{35}\right)^2=\left(\dfrac{6}{7}\right)^2=\dfrac{36}{49}\)
d: \(\left(\dfrac{1}{9}\right)^2:\left(\dfrac{1}{3}\right)^3=\left(\dfrac{1}{3}\right)^4:\left(\dfrac{1}{3}\right)^3=\dfrac{1}{3}\)
e: \(\left(-\dfrac{1}{2}\right)^3\cdot\left(\dfrac{3}{2}\right)^3=\left(-\dfrac{1}{2}\cdot\dfrac{3}{2}\right)^3=\left(-\dfrac{3}{4}\right)^3=-\dfrac{27}{64}\)
f: \(125\cdot5^2\cdot5^0=5^3\cdot5^2=5^5=3125\)
