\(a.\left(\dfrac{1}{2}\right)^5\cdot\left(\dfrac{1}{4}\right)^2=\left(\dfrac{1}{2}\right)^5\cdot\left(\dfrac{1}{2}\right)^4=\left(\dfrac{1}{2}\right)^9=\dfrac{1}{512}.\)
\(b.\left(\dfrac{5}{4}\right)^2:\left(-\dfrac{35}{24}\right)^2=\dfrac{25}{16}:\dfrac{1225}{567}=\dfrac{25}{16}\cdot\dfrac{567}{1225}=\dfrac{36}{49}.\)
\(c.\left(-\dfrac{1}{2}\right)^2\cdot\left(\dfrac{2}{5}\right)^2=\dfrac{1}{4}\cdot\dfrac{4}{25}=\dfrac{1}{25}.\)
\(d.25\cdot5^{-1}\cdot5^0=25\cdot\left(5^{-1}\cdot5^0\right)=25\cdot5^{-1}=25\cdot\dfrac{1}{5}=5.\)
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