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$\left(\dfrac{\cancel{46}^2}{\cancel{63}_3}ab^4c\right)·\left(\dfrac{\cancel{42}^2}{\cancel{23}_1}a^3b\right)·\left(-\dfrac{9}{8}abc^3\right)=$
$=\left(\dfrac{2}{3}ab^4c\right)·\left(\dfrac{2}{1}a^3b\right)·\left(-\dfrac{9}{8}abc^3\right)=$
$= \dfrac{4}{3}a^4b^5c·\left(-\dfrac{9}{8}abc^3\right) =$
$= \dfrac{\cancel4^1}{\cancel3_1}a^4b^5c·\left(-\dfrac{\cancel9^3}{\cancel8_2}abc^3\right) =$
$= -\dfrac{3}{2}a^5b^6c^4$