This paper investigates cosmological solutions in the context of the modified $ f(R, T) $ gravity theory, focusing on the bouncing universe scenario. The study considers the Friedmann-Robertson-Walker (FRW) spacetime and explores various cosmological models, including acceleration expansion, ultra-relativistic, sub-relativistic, dust, radiation, and stiff universes. Two different $ f(R, T) $ gravity models are analyzed using the power law technique to observe the expanding nature of the universe. The bouncing scenario is examined by choosing specific model parameters and verifying the satisfaction of energy conditions, which are essential for a successful bouncing model. The results indicate that some solutions in $ f(R, T) $ gravity support the concept of exotic matter and accelerated expansion due to a large amount of negative pressure. The paper also discusses the bouncing cosmology in $ f(R, T) $ gravity, highlighting the violation of energy conditions, particularly the null energy condition (NEC), around the bouncing point. This violation allows for the presence of exotic matter, which drives the contraction and subsequent expansion of the universe. The analysis shows that the negative pressure component supports the presence of exotic matter, crucial for the universe's expansion. The study concludes that the proposed $ f(R, T) $ gravity model provides good bouncing solutions with the chosen equation of state (EoS) parameters. The results suggest that the model is viable and supports the concept of a bouncing universe, offering an alternative framework to the traditional big bang singularity.This paper investigates cosmological solutions in the context of the modified $ f(R, T) $ gravity theory, focusing on the bouncing universe scenario. The study considers the Friedmann-Robertson-Walker (FRW) spacetime and explores various cosmological models, including acceleration expansion, ultra-relativistic, sub-relativistic, dust, radiation, and stiff universes. Two different $ f(R, T) $ gravity models are analyzed using the power law technique to observe the expanding nature of the universe. The bouncing scenario is examined by choosing specific model parameters and verifying the satisfaction of energy conditions, which are essential for a successful bouncing model. The results indicate that some solutions in $ f(R, T) $ gravity support the concept of exotic matter and accelerated expansion due to a large amount of negative pressure. The paper also discusses the bouncing cosmology in $ f(R, T) $ gravity, highlighting the violation of energy conditions, particularly the null energy condition (NEC), around the bouncing point. This violation allows for the presence of exotic matter, which drives the contraction and subsequent expansion of the universe. The analysis shows that the negative pressure component supports the presence of exotic matter, crucial for the universe's expansion. The study concludes that the proposed $ f(R, T) $ gravity model provides good bouncing solutions with the chosen equation of state (EoS) parameters. The results suggest that the model is viable and supports the concept of a bouncing universe, offering an alternative framework to the traditional big bang singularity.