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In the next generation wireless communication paradigm, the number of devices are expected to increase exponentially after the concept of Internet of Things (IoT). These devices are power constrained, with limited processing capability. Therefore, in order to get the maximum advantage from these low power IoT sensing devices, it is of utmost need to empower them. Similarly, the devices are not able to process the computationally intensive applications. In this work, Wireless Power Mobile Edge Cloud (WPMEC) is considered, which is an integration of Wireless Power Transfer (WPT) and Mobile Edge Cloud (MEC) to address low power devices' battery and computational capabilities. The WPMEC is charging the devices in the first phase using the WPT and in the second phase, the devices are offloading their computational intensive data to the MEC. Partial offloading scheme is first time introduced and analyzed with WPMEC. Performance of proposed solution is evaluated in terms of overall network computational energy efficiency. Extensive simulations have been carried out to validate the proposed solution. It is shown that the proposed partial offloading scheme with WPMEC outperforms the binary and local computational schemes.