Images captured by cameras with incorrect exposure settings typically suffer from degradations in multiple aspects, including brightness, color, and structure. Existing methods often obtain a normally exposed image by fusing images with varying exposures. However, these methods need to calculate the exposure representations of different images, which increases the computational burden. Some other models work on correcting the underexposures of a single image. However, the large differences between different exposures may cause the poor generalization. In this paper, we propose a unified exposure correction network (MECNet), the core of which is an exposure normalization and adaptive transfer (ENAT) block. Specifically, ENAT block employs normalization to align different exposures, and transfers the information unaffected by abnormal exposures to mitigate the normalization effects. We also introduce the shuffle attention to establish communication between multiple-exposures, and make the model more focused on areas with abnormal exposures. In addition, we also design a residual-guided feature calibration (RGFC) block for the up and down sampling layers, which can control the flow of information at different scales. Extensive experiments demonstrate that our method achieves competitive performance while maintaining a low amount of parameters, and can be applied to other enhancement tasks, proving the potential and effectiveness in visual tasks.