The modern numbering system and the zero were both mathematical innovations made within which empire? Aksum
China
Gupta
Mauryan

Gupta Empire.

Explanation:

The Gupta Empire was one of the empires established in India and was in existence during the late 3rd century CE. The period was also known as the Golden Age of the Indian empire for the different developments and innovative discoveries during this period.

The numbering system as well as the concept of zero were invented by Aryabhatta, an Indian astronomer, during this period. Many other advancements such as the discovery of the different planets, the calculations of the solar and lunar eclipses, the approximate value of pi, negative numbers, calculation of square roots, etc were also seen during this period.

Thus, the correct answer is the Gupta empire.  

executive, (president and about 5,000,000 workers) legislative (senate and house of representatives) and judicial (supreme court and lower courts)

explanation:

radioactive dating, also known as  radioisotope dating  is a process that in  estimating the approximate  age  of  rocks. these data can be analyzed from  the studies dealing with the  decay of the radioactive elements that are present in these rocks. in nature, there are a few types of materials or atoms which are quite unstable and they spontaneously decay or breakdown to form other kinds of atoms.