\(\left(\dfrac{23}{12}\right)^{2021}.\left(\dfrac{12}{23}\right)^{2022}\\ =\left(\dfrac{23}{12}\right)^{2021}.\left(\dfrac{12}{23}\right)^{2021}.\dfrac{12}{23}\\ =\left(\dfrac{23}{12}.\dfrac{12}{23}\right)^{2021}.\dfrac{12}{23}\\ =1^{2021}.\dfrac{12}{23}\\ =1.\dfrac{12}{23}\\ =\dfrac{12}{23}\)