Simplify $\dfrac{24m^5}{7m^{17}}\cdot\dfrac{49m^{19}}{18m^3}\cdot\dfrac{3m^{-2}}{4m}$
Strike out the 7
then you have
24 * 7 * 3 / (18 * 4)
cancel out the 4
6 * 7 * 3 / (18) cancel out the 6
7 *3 / 3 cancel out the 3
= 7 m (5 + 19 -2 -17-3-1) = 7 m
Strike out the 7
then you have
24 * 7 * 3 / (18 * 4)
cancel out the 4
6 * 7 * 3 / (18) cancel out the 6
7 *3 / 3 cancel out the 3
= 7 m (5 + 19 -2 -17-3-1) = 7 m