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Traditional routing algorithms tend to use shortest path algorithms with minimum hop count to reduce transmission latency and error rates, resulting in a quick exhaustion of a small subset of nodes where the traffic load is heavy and risking a disconnection of the entire network. We define a new power-aware cost metric with the aim of reflecting both power-saving perspectives: maximizing network lifetime and minimizing the power consumption of a routing task. We also propose a new location-aided, power-aware routing protocol that is based on a combination of greedy and multicasting strategies. The decision on applying greedy or multicasting within its routing zone depends on the link cost and the node's neighborhood distribution. Simulation results show that performances on network lifetime and average power consumption for routing tasks are greatly improved without sacrifices in the delivery rate of the ad hoc network.