Yes, there is. There is a law of exponentiation. # The definition of exponentiation shows us it is a product, but the law of exponentiation shows us it is a sum. # Law of exponentiation is confirmed by a general formula to be expressed by words. # From there one sees exponentiation to be constructed by the two constants: base constant and exponent constant. It is the property of exponentiation. Author Đoàn Đức Nhuận (in vietnamese)

There isn't one. It is an algebraic operation, not an arithmetic one and is called exponentiation.

Of or pertaining to mode, modulation, module, or modius; as, modular arrangement; modular accent; modular measure.

Difference between modular and non-modular bricks

That may be a mis-spelling of "exponentiation".