The power wall is one of the primary stumbling blocks that many-core microprocessor architecture is facing today. To avoid this problem, microprocessor makers are shifting towards heterogeneous chips that integrate different core architectures on a single die and that have proved to deliver better performance per watt. Moreover, these new hybrid microprocessors are equipped with dynamic frequencyscaling techniques that are capable of reducing total system power consumption.This paper presents a theoretical study on how performance and power consumption are affected by the dynamic frequency-scaling techniques offered by the power constraints imposed on state-of-the-art dual-architecture processors. Analytical schemes have been developed to extend Amdahl's Law by accounting for energy limitations before examining the three processing schemes available to heterogeneous processors: symmetric, asymmetric, and simultaneous asymmetric. Analysis shows that by choosing the optimal chip configuration, power efficiency and energy savings can be increased considerably while keeping sacrifices in performance at tolerable levels.