According the zheng he what are the purposes of the ming voyages

To establish trade relationships, explore new lands, and increased China's influence.

Explanation:

Under admiral Zheng He, China got hold over the Indian Ocean in the 15th century. He went to several expeditions and opened trading connection with South Asia. In Asia, he conducted trade in south Asia by exporting silk and porcelain in return for other goods. Silk during the early years recognised as a luxury thing and worn by the aristocracy, including emperors and nobles.  

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