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\(a)\dfrac{5^4.20^4}{25^5.4^5}=\dfrac{\left(5.20\right)^4}{\left(25.4\right)^5}=\dfrac{100^4}{100^5}=\dfrac{1}{100}\)
\(b)\dfrac{3}{8}.19\dfrac{1}{3}-\dfrac{3}{8}.33\dfrac{1}{3}=\dfrac{3}{8}.\left(19\dfrac{1}{3}-33\dfrac{1}{3}\right)=\dfrac{3}{8}.\left(-14\right)=-\dfrac{21}{14}\)
\(c)\dfrac{13}{25}+\dfrac{6}{41}-\dfrac{38}{25}+\dfrac{35}{41}-\dfrac{1}{2}\)
\(=\left(\dfrac{13}{25}-\dfrac{38}{25}\right)+\left(\dfrac{6}{41}+\dfrac{35}{41}\right)-\dfrac{1}{2}\)
\(=-\dfrac{1}{2}\)
\(d)12.\left(-\dfrac{2}{3}\right)^2+\dfrac{4}{3}=\dfrac{16}{3}+\dfrac{4}{3}=\dfrac{20}{3}\)
\(e)12,5.\left(-\dfrac{5}{7}\right)+1,5.\left(-\dfrac{5}{7}\right)=\left(12,5+1,5\right).\left(-\dfrac{5}{7}\right)=-10\)
\(f)\dfrac{4}{5}.\left(\dfrac{7}{2}+\dfrac{1}{4}\right)^2=\dfrac{4}{5}.\dfrac{225}{16}=\dfrac{45}{4}\)
