Learning to process long-range dependencies has been a challenge for recurrent neural networks. Despite improvements achieved by long short-term memory (LSTMs), its gating mechanism results in exponential decay of information, limiting their capacity of capturing long-range dependencies. In this work, we present a power law forget gate, which instead has a slower rate of information decay. We propose a power law-based LSTM (pLSTM) based on the LSTM but with a power law forget gate. We test empirically the pLSTM on the copy task, sentiment classification, and sequential MNIST, all with long-range dependency tasks. The pLSTM solves these tasks outperforming an LSTM, specially for long-range dependencies. Further, the pLSTM learns sparser and more robust representations.