Abstract
Exponents are at the heart of our understanding of certain mathematics-dependent concepts
such as population growth, compound interest, and radioactive decay. However, exponents remain
challenging to learn. As a result, students make errors when working with problems involving simplifying
exponents. This article describes students’ thinking about the errors they and their peers make when
simplifying exponential expressions. Understanding students’ thinking behind their errors is essential for
teachers to provide constructive feedback. A purposive sample of forty-two first-year engineering students
was selected from one of South Africa’s public universities located in the Gauteng Province. Qualitative data
were generated using a mathematics test compiled by researchers, students’ written answers to the
mathematics test, students’ performance marks, and students’ responses to group interviews. The findings
of this study indicated that students’ explanations of their thinking about the errors they make can be
divided into four categories: mixing of exponential rules with algebra rules, misapplication of exponential
rules, distribution error, and factorization error.