Audio editing involves the arbitrary manipulation of audio content through precise control. Although text-guided diffusion models have made significant advancements in text-to-audio generation, they still face challenges in finding a flexible and precise way to modify target events within an audio track. We present a novel approach, referred to as PPAE, which serves as a general module for diffusion models and enables precise audio editing. The editing is based on the input textual prompt only and is entirely training-free. We exploit the cross-attention maps of diffusion models to facilitate accurate local editing and employ a hierarchical local-global pipeline to ensure a smoother editing process. Experimental results highlight the effectiveness of our method in various editing tasks.