An exponent is the number in superscript on the right side of the variable. For example, x², x is the variable and 2 is its exponent. To divide variables with exponents, all we need to do is to complete the subtraction of the exponents of the SAME VARIABLE, and the subtraction result will become the new exponent. For example:

x⁶ ` ``-:` x³ = x³                 

Here, the exponents are 6 and 3. We only have x as variable here, so by doing the subtraction 6-3 we get 3 as exponent.

This is same as x⁶` `` ` / x³ = x³           (Because devision can be expressed as fraction.)

What about x⁶ `-:` x³ `-:` y²?

Since x and y are different variables, we can't add up their exponents. So we only get x³ / y².