We study the role of task-level scheduling in power management on multicore multiple voltage embedded systems. Multicore on-a-chip, in particular DSP systems, can greatly improve performance through parallelism. On the other hand, dynamic voltage scaling (DVS) has been shown to be one of the most effective low power design techniques and multiple supply voltage system is among the most practical and well-studied DVS systems. The integration of multiple cores/processors on a chip naturally makes the system suitable for DVS with new innovations such as voltage island. In this paper, we discuss how to reduce multicore system?s power consumption by utilizing multiple supply voltages. We first formulate the power management problem for multicore multi-voltage embedded systems and show that the problem is NP-hard, but the NPhardness can be removed for several real life applications. More specific, we develop polynomial algorithms to find the optimal solutions for two special cases. The first case is when preemption is allowed, and the second one is when the system uses the first-come-first- serve (FCFS) service strategy. We prove both algorithms? optimality and analyze their run-time complexity. Simulation on reallife and randomly generated tasks show that the optimal preemption scheduler provides significant energy saving. Our goal in this paper is to build a solid foundation for the power management problem on multicore multiple voltage systems and to study real life applications where the problem can be solved optimally.