Final answer:
The Silk Roads encouraged the growth of Sogdiana by facilitating trade and cultural exchanges, thereby fostering economic prosperity and cultural transformation in the region.
Step-by-step explanation:
The Silk Roads played a crucial role in encouraging the growth of Sogdiana by facilitating trade and cultural exchanges. These trade routes connected the East and West, allowing Sogdian city-states like Samarkand and Panjikent to become key markets where commodities such as hides, wool, and livestock from the Central Asian steppes were exchanged for Chinese manufactured goods, which were then traded along the Silk Roads to reach distant markets.
Moreover, the rise of the Islamic caliphate and its control over portions of the Silk Roads led Sogdian merchants and traders to convert to Islam, thereby gaining the benefits of reliable contracts among believers to safeguard their goods along the trading routes. This resulted not only in the economic prosperity of Sogdiana but also in significant cultural transformations due to the influence of Islam. Therefore, the correct answer to the question 'How did the Silk Roads encourage the growth of Sogdiana?' is c) By facilitating trade and cultural exchanges, fostering economic prosperity.