In this article, a mathematics teacher educator presents an activity designed to pique the interest of prospective secondary mathematics teachers who may doubt the value of learning abstract algebra for their chosen profession. Herein, he contemplates: what "is" intended by the widespread requirement that high school mathematics teachers study abstract algebra, or for that matter linear algebra, real or complex analysis, or topology? He goes on to explain how through what seemed like sheer chance, he gained much from abstract algebra: an understanding and appreciation of mathematical structure, a sense of the relationship between flexible examples and formalized generalities, and a recognition of the need for rigor. He then asks: thinking as a teacher educator, what if this kind of experience could be built-in and planned rather than simply left to chance and hoped for? It is in light of this question that he developed an activity called "The Power of Powers of 3" The activity begins with a table of integer powers of 3, from 0 through 24, as the teacher explains that powers of 3 have a very useful property. That useful property is that multiplication of some numbers can be performed by the addition of the corresponding numbers in the table. This is followed by the introduction of logarithms as an isomorphism (a relationship that allows a person to correctly compute something difficult by converting the product into an easier calculation and then converting the result back after it is computed).