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1: \(\dfrac{4}{23}+\dfrac{5}{21}+\dfrac{1}{2}-\dfrac{4}{23}+\dfrac{16}{21}\)
\(=1+\dfrac{1}{2}\)
\(=\dfrac{3}{2}\)
2: \(\left(\dfrac{1}{3}+\dfrac{12}{67}+\dfrac{13}{41}\right)-\left(\dfrac{79}{67}-\dfrac{28}{41}\right)\)
\(=\dfrac{1}{3}+\dfrac{12}{67}+\dfrac{13}{41}-\dfrac{79}{67}+\dfrac{28}{41}\)
\(=\dfrac{1}{3}\)
\(\frac{2^{10}.9^{41}.25^{23}}{3^{50}.15^{35}.10^3}\)=\(\frac{2^{10}.\left(3^3\right)^{41}.\left(5^2\right)^{23}}{3^{50}.\left(3.5\right)^{35}.\left(2.5\right)^3}\)=\(\frac{2^{10}.3^{123}.5^{46}}{3^{50}.3^{35}.5^{35}.2^3.5^3}\)=\(\frac{2^{10}.3^{123}.5^{46}}{3^{85}.5^{38}.2^3}\)=\(2^7.3^{38}.5^8\)