Final answer:
The rapid technological advancement of the 19th century was most significantly influenced by the development of steam power, which enabled industrial growth and urbanization. This advancement laid the groundwork for further important industrial changes like electric power production and efficient steel manufacturing.
Step-by-step explanation:
The most significant factor influencing the rapid technological advancement of the 19th century was the development of steam power (A). The advent of steam technology enabled unmatched industrial growth, transforming how work was done in both farms and factories. Critically, steam power allowed industries to move away from water sources and relocate production into cities, which supported the urbanization of the population.
Additionally, steam technology paved the way for subsequent industrial advancements such as electric power production and steel manufacturing, which were also significant developments of the time. The ability to produce large steel elements efficiently and affordably, further advanced by processes like the Bessemer and open-hearth methods, significantly impacted business growth and industrialization.
Thus, while individuals like Thomas Edison and innovations in communication technologies played important roles, it was the fundamental change in energy production and use, leveraged through steam, that most influenced the era's rapid technological progression.