The answer is: As Persian control expanded, the empire had access to more resources, which Darius was then able to use to construct his new capital.
This is a defensible historical claim. As the Persian Empire expanded under Darius I, it gained access to a wealth of resources from the newly conquered territories. These resources, including materials, labor, and wealth, were crucial in the construction of Persepolis. The expansion of the empire provided the necessary means to undertake such a grand project, making this option a logical connection between imperial expansion and the construction of Persepolis.
This claim is not supported by historical evidence. The construction of Persepolis did not cause the Persian Empire to shrink. In fact, the empire continued to expand during and after the construction of Persepolis. The allocation of resources to build the capital did not significantly detract from the empire's ability to maintain and expand its frontiers.
This option is not accurate. The construction of Persepolis was closely related to the expansion of the Persian Empire. The resources and wealth acquired through imperial expansion were directly used to fund and build the new capital. Therefore, it is incorrect to say that the construction of Persepolis was unrelated to the empire's expansion.
While the construction of Persepolis did symbolize the power and grandeur of the Persian Empire, it is not accurate to claim that it directly allowed them to conquer more territory. The expansion of the empire was more directly influenced by military campaigns, strategic alliances, and effective governance rather than the mere appearance of power through the construction of a capital.