how did the persians build a strong empire
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Per the question in your picture:
Answer:
C-Athens had defeated Persia at the Battle of Salamis, so Persia supported Sparta.
Explanation:
The Peloponnesian Wars were between Athens and Sparta (Greek). Persia supported Sparta because Athens had defeated Persian so they became allies with Sparta.
How did the persians build a strong empire? By using a common currency