Explain the difference in dividing coefficients in front of like bases and dividing the exponents attached to the like bases

This is easier to explain and understant with an example

Suppose these two exponents, with like bases: 12a^4 and 4a^2

The division is (12a^4) / (4a^2).

The procedure is copy the base, divide the coefficientes and subtract the exponent of the denominator base from the exponent of the numerator base:

12 / 4 = 3

4 - 2 = 2

Result = 3a^2.

Then, the coefficients are divided and the exponents are subtracted.

In a general case: (A x^m ) / (Bx^n) = [A/B] x^ (m-n).

With a continuous thought process.