Only China modeled their political systems after the earlier precedents set by the Xia, Shang, and Zhou; whereas Rome created a new political system for their empire without such precedents. It is true that both empires existed around the same time in the Classical era. Rome and China both relied on military force for the purpose of empire-building, and both invested heavily on public works projects.

One of the primary ways Rome was able to create such a massive empire was through its equally massive, disciplined, and technologically advanced army. Cultural diffusion did not necessarily allow Rome to conquer and expand its empire, but was rather a consequence of empire expansion. Rome did not regularly use diplomacy in empire-building. Though Rome was centrally located within the empire, this does not explain how they conquered.

Political fragmentation and cultural diversity made the creation of centralized empires less common in India than in China. The Indian subcontinent was politically fragmented since the fall of the Mauryan Empire in 184 BCE. That, along with a great deal of cultural diversity, made it difficult to unify India under one centralizing force. Few people in India practiced a nomadic lifestyle by the Classical era. Also, most Indians were united by the caste system and Hinduism, so clashing religious beliefs would not have been a dividing factor. 

Muscovites worked as tribute collectors for the Mongols, which increased their wealth and power. Mongolians killed the Abbasid caliph in 1258, defeated the Song, promoted religious tolerance, and did not end serfdom. 

Zheng He was the admiral in charge of leading several large expeditions of Ming dynasty 'treasure fleets' throughout the Indian Ocean and East Asian coasts during the 15th century.  His journeys helped to establish in the minds of many contacted peoples the might of Imperial China, while confirming for many Chinese bureaucrats the power of the Ming dynasty.

The Mongols were unable to conquer the interior of Vietnam because the dense jungle made it nearly impossible for Mongol cavalry to operate effectively.

The Mongols were able to conquer Afghanistan by destroying the Afghan irrigation system, turning much of the once fertile country into barren wasteland and depriving the Afghan resistance of irrigation tunnels used to transport fighters and weapons.

After heavy fighting, the Mongols conquered China and proclaimed the Yuan dynasty.

The Mongols were able to conquer much of the Arab world by using ingenious siege tactics against large cities.

The Mongols were able to conquer and destroy much of modern Russia, including Moscow.

Viking colonization of Russia was so successful that hundreds of years later Russian royalty was still descendant from the original invaders.

The Vikings never colonized China; it was too far for them to travel, and most likely too well defended for them to successful conquer even if they'd tried.

The Vikings never reached Japan, let alone attempted to colonize it.

Unlike in Russia, Viking settlements in North America were not successful and died out relatively quickly.

Afghanistan is a landlocked country whereas the Vikings were seaborne raiders and colonists; conquering Afghanistan would have been nearly impossible for them even if they'd tried.

The great typhoons that twice destroyed the Mongol navy were called Kamikaze by the Japanese, meaning divine winds.

Kamehameha was a Hawaiian king who successfully defended Hawaii independence from European colonial expansion; his name has become synonymous with special powers in Japanese comic books, but he had nothing to do with the failed Mongol invasions of Japan.

El Nino is an aquatic phenomenon comprised of warming Pacific Ocean temperatures that has nothing to do with the defeat of the Mongol invasion force.

The Trade Winds are a longstanding pattern of wind that the early European colonial powers, especially Spain and Portugal, used in their naval campaigns; the trade winds had nothing to do with the Mongol's defeat in Japan.

The Miracle of the House of Brandenburg had nothing to do with the Mongol invasion of Japan. The "miracle" occurred after Prussia had been defeated by a combined Austrian-Russian attack; rather than follow up their victory, the Austrians and Russians withdrew, saving Prussia for the time being.

The Visigoth kingdom on the Iberian peninsula was conquered by a Muslim force of Arabs, Berbers, and other Africans who sailed from North Africa to Gibraltar.

Communism would not come to exist for over another thousand years, and though the Spanish civil war of the 20th century featured Communists, they eventually lost to fascist forces.

Napoleon Bonaparte invaded Spain during the early 19th century, over a millennia after Visigoth culture ceased to exist, and although his invasion was very bloody, it was not very successful.

The British navy did conduct operations in Spain, capturing Gibraltar, but this was in the early 18th century and against the Spanish government, not the Visigoth kingdom.

The Spanish-American war was fought at the very end of the 19th century in the Pacific and Caribbean; at no point did any of the Iberian peninsula become a battlefield.

Mali's time as a hegemonic power in West Africa was relatively short lived and their fall from grace coincided with the rise of the Songhai Empire. The Songhai Empire was centered around its capital in Gao. The height of the Songhai Empire was the fifteenth and early sixteenth centuries. The most famous rulers of Songhai were Askia and Sunni Ali.