a: \(=\left(1+\dfrac{4}{23}-\dfrac{4}{23}\right)+\left(\dfrac{5}{21}+\dfrac{16}{21}\right)+\dfrac{1}{2}=1+1+\dfrac{1}{2}=2+\dfrac{1}{2}=\dfrac{5}{2}\)
b: \(=\dfrac{5}{6}\left(\dfrac{4}{9}-\dfrac{3}{5}+\dfrac{5}{9}+\dfrac{1}{5}\right)=\dfrac{5}{6}\cdot\left(1-\dfrac{2}{5}\right)=\dfrac{5}{6}\cdot\dfrac{3}{5}=\dfrac{3}{6}=\dfrac{1}{2}\)
c: \(=\dfrac{100}{123}:\dfrac{9+7}{12}+\dfrac{23}{123}:\dfrac{27-7}{15}\)
\(=\dfrac{100}{123}\cdot\dfrac{12}{16}+\dfrac{23}{123}\cdot\dfrac{15}{20}\)
\(=\dfrac{3}{4}\left(\dfrac{100}{123}+\dfrac{23}{123}\right)=\dfrac{3}{4}\)
d: \(=\dfrac{3^{16}\cdot2^{18}}{2^{16}\cdot3^{17}}=\dfrac{1}{3}\cdot4=\dfrac{4}{3}\)
