Final answer:
Legislatures face challenges such as political polarization, lack of public support, and bureaucratic inefficiency in exercising their powers.
Step-by-step explanation:
Legislatures face several challenges in exercising their legitimate powers. One challenge is political polarization, which refers to the increasing divide between different political parties or factions. This can make it difficult for lawmakers to reach consensus and pass legislation. Another challenge is lack of public support, which can undermine the legitimacy and effectiveness of a legislature. Finally, bureaucratic inefficiency is another challenge, as the complex bureaucratic processes can slow down the implementation of legislative actions.