You need to turn
[tex]14m ^{2} {a}^{3} m \\ \div \\ 21 {a}^{2} {m}^{4} [/tex]
into the simplest form. To do this, you must first find all instances of each variable. Then simplify the constant.
First, find M in both the numerator and denominator. In the numerator, there is M^2 and m, therefore, there are 3 Ms. In the denominator, there is M^4, so there are 4 Ms. Then, since 4 > 3, you subtract 3 from 4, and put the remainder in the denominator (since the 4 is from the denominator).
Second, find all of the As. There are 3 As in the numerator, and 2 in the denominator. Since 3 is bigger, we subtract and are left with 1 A in the numerator.
Third, find the numbers. There is a 14 in the numerator and a 21 in the denominator. 14 = 2 × 7, and 21 = 3 × 7, so both the numerator and denominator have a factor of 7, so you can cancel out the 7s. This leaves you with 2 on top and 3 on bottom.
The final solution then turns out to be:
[tex]2a \\ \div \\ 3m[/tex]
