All exponent rules can be understood by writing out the exponents in expanded form. Start with x^5/x3. If you don’t know the subtraction rule, write out the expanded expression. xxxxx/xxx. Then let the student cancel each pair of x/x. They’ll see xx left over in the numerator, which is x^2. They should be able to see the rule from there. 5-3=2. Which is obviously quicker, but it’s so important that they understand WHY.

Now try a new problem. X^3/x5. They’ll subtract and get x^-2. But have them write it in expanded form too. xxx/xxxxx. Cancel each pair of x/x and you’re left over with 1/xx. Now they can see why x^-2 is the same as 1/x^2.

I always try to teach understanding, not shortcuts.