Power differences shape human communication through well-documented socio-cognitive effects, including language coordination, pronoun usage, authority bias, and harmful compliance. We examine whether large language models (LLMs) exhibit similar behaviors when assigned high- or low-status personas. Using personas from diverse professions, we simulate multi-turn, power-asymmetric dialogues (e.g., principal–teacher, justice–lawyer) and measure (i) linguistic coordination, (ii) pronoun usage, (iii) persuasion success, and (iv) compliance with unsafe requests. Our results show that LLMs show key socio-cognitive effects of power, albeit with nuances and variability, linking simulated interactions to both desirable and unsafe behaviors.