In recent decades, power consumption has become an essential factor in attracting the attention of integrated circuit (IC) designers. Multiple-valued logic (MVL) and approximate computing are some techniques that could be applied to integrated circuits to make power-efficient systems. By utilizing MVL-based circuits instead of binary logic, the information conveyed by digital signals increases, and this reduces the required interconnections and power consumption. On the other hand, approximate computing is a class of arithmetic computing used in systems where the accuracy of the computation can be traded-off for lower energy consumption. In this paper, we propose novel designs for exact and inexact ternary multipliers based on carbon-nanotube field-effect transistors (CNFETs). The unique characteristics of CNFETs make them a desirable alternative to MOSFETs. The simulations are conducted using Synopsys HSPICE. The proposed design is compared against existing ternary multipliers. The results show that the proposed exact multiplier reduces the energy consumption by up to 6 times, while the best inexact design improves energy efficiency by up to 35 time compared to the latest state-of-the-art methods. Using the imprecise multipliers for image processing provides evidence that these proposed designs are a low-power system with an acceptable error.