Simplify $\frac{3a^2b}{5ac}\times\frac{10c}{6ab}$, given that $a,b,c\neq0.$
To simplify this expression, I can use the rules of fractions and exponents to multiply the numerators and the denominators, and then simplify the common factors. Multiplying the numerators, I get $3a^2b\times10c=30a^2bc$. Multiplying the denominators, I get $5ac\times6ab=30a^2bc$. So the expression becomes $\frac{30a^2bc}{30a^2bc}$. Now I can cancel out any common factors in the numerator and denominator, as long as they are not zero. I see that $30, a^2, b, c$ are all common factors, so I can divide both the numerator and denominator by them. This leaves me with $\frac{30a^2bc}{30a^2bc}=\frac{1}{1}$. Finally, I can simplify $\frac{1}{1}$ to $1$. 