The multiplication operator is very important in algebra and number theory. Tied to it is the property of primality. A number that is prime can only be written as a product of 1 and itself and not as product between any other numbers.
The power operator is iterated multiplication: $$n^m = \underset{\text{m times}}{\underbrace{n\cdot n \cdots n}}$$
Would it make sense to call a number $a$ which can not be written as $b^c$ in any other way than $a^1$ a power prime? Would it have any important uses in number theory or elsewhere?