jmc

We multiply fractions by multiplying their numerators and denominators. The given expression, $\frac{3a^{2}b}{5ac}\times \frac{10c}{6ab}$, becomes $\frac{3a^{2}b\cdot 10c}{5ac\cdot 6ab}=\frac{30a^{2}bc}{30a^{2}bc}=\boxed{1}$, since any nonzero number divided by itself is 1.