Why Exponents Subtract

Write x^6 / x^2 out in full and watch the cancellation happen: six factors of x over two. The fraction x/x is 1 whenever x is not zero, so each bottom factor pairs with a top factor and the pair disappears, leaving a factor of 1 that changes nothing.

Two pairs cancel; four factors of x remain upstairs, untouched: x^6 / x^2 = x^4. The subtraction 6 - 2 never touched the values; it counted the factors that survived the pairing.

This picture is the one to keep, because it explains the rule's edge cases before you meet them: what happens when top and bottom have equal counts, and what happens when the bottom has more. Both answers fall out of the same pairing, later, in the chapter on zero and negative exponents.