Describe how each of the following innovations affected the tang and song dynasties, as well as today: printing, gunpowder and rockets, the compass, the moveable type, smallpox inoculate, steel, tea and porcelain

Printing enable the Chinese dynasties to create a large, structured government to include contracts and legal documents as well as aided in the historical development of the empires. However the first printing method was slow and limited. When the Chinese developed moveable type, printing could be sped up and increased the volume of printed materials available. This type of printing will enable the printing of books and increased educational opportunities as literacy rates increased. 
Gunpowder was initially created to be an immortality potion. Ironically it ended the life of the creator when it blew up and has since ended the lives of millions in warfare. Gunpowder was used in China for fireworks and rockets but was eventually developed to be used for weaponry including canons and guns. This will change how wars are fought throughout the world. 
The compass will allow for travel through the seas enabling the boats to arrive at a destination and return safely. The Chinese are now suspecting as being explorers centuries before the Europeans and were likely the first outsiders to encounter the western parts of the Americas. The compass will eventually make way to Europe leading to an age of exploration beginning in the 15th century. 
Steel, tea, and porcelain were marketable resources for China allowing them to create large trade networks. Steel created structures, porcelain created durable dinnerware and statues, and tea was a clean and safe drink. All of these products will help to create the Silk Road trade network as well as water-based trading enabled by the compass. 
Lastly, inoculation technology improved the health of the Chinese eradicating diseases which were still killing European populations. This technology became the basis for vaccinations which today have reduced plagues, poxes, and as well as many other deadly diseases.