A repeated percentage change means the same kind of percentage change happens more than once, each time on the new amount. The quickest method is to turn the percentage into a multiplier.

For an increase of $p\%$, use $1+\frac{p}{100}$. For a decrease of $p\%$, use $1-\frac{p}{100}$. For example, a 12% increase gives a multiplier of $1.12$, while a 12% decrease gives $0.88$.

If the same multiplier $m$ happens $n$ times, the overall multiplier is $m^n$. That is why repeated percentage change is really about multipliers, powers, and sometimes roots.