What System is based on the power of ten?

The metric system

It works in powers of 10, so figures such as 100 and 1000 are especially important. There are 100 centimetres in a metre and 1000 metres in a kilometre for example.

metric system!

yes, nothing prevents you from having exponents that also have exponents. In the case that you ask about, of ten to the ten to the ten, that would be better expressed as ten to the ten billion, or...