The negative sign and exponential expressions: Unveiling students' persistent errors and misconceptions

The purpose of this study was to determine whether or not certain errors made when simplifying exponential expressions persist as students progress through their mathematical studies. College students enrolled in college algebra, pre-calculus, and first- and second-semester calculus mathematics courses were asked to simplify exponential expressions on an assessment. Persistent errors are identified and characterized. Using quantitative and qualitative methods, we found that the concept of negativity played a prominent role in most of the students' errors. We theorize that an underdeveloped conception of additive and multiplicative inverses is the root of these errors.