Hello everybody!

This is my 1st question in this forum.

I have passed just high-school level mathematics, so I would appreciate an answer that is understandable to such educational level of a person.

Time to time they say in popular science math books, that a large exponent number is such and such in length, for example 3^7146 contains 1846678925 integers or so (this is not a real example, I just put those numbers in screen here). They may also tell us that the last integer is, say, "9".

I would like to know, what kind is an algorithm they really use in their computers? It is hard for me to believe that they use naive repetitive multiplications time after time?

My question consearns expecially integer or natural number base numbers and exponents.