The Rule in Letters

The quotient rule written with letters is a^m / a^n = a^(m-n). It holds for any base a and any exponents m and n. The exponent on top minus the exponent on the bottom gives the number of factors that are left.

Look at the right side carefully. The whole difference m - n is the exponent, so when you write it on one line it needs parentheses: a^(m-n). Without them, a^m - n means the power a^m with n subtracted from it, which is a different expression.

Together with the product rule, a^m * a^n = a^(m+n), you now know the two laws for multiplying and dividing powers with the same base. The next chapter adds a third law, for a power raised to a power.