What is 1 billion multiplied by 1 billion?

Some countries assign different meanings to the Word billion; I'll assume that you want your answer in the short scale, which is used in most English-speaking countries.

1 billion on the short scale = 10 to the power of 9 = 10^9

10^9 * 10^9 = 10^18 = 10 to the power of 18 = 1 quintillion on the short scale.