1. The problem is to understand and express the operation $M^N$ where $M$ and $N$ typically denote numbers or variables, and the caret symbol $^$ indicates exponentiation. 2. Exponentiation means multiplying the base $M$ by itself $N$ times if $N$ is a positive integer. 3. Mathematically, this is: $$M^N = \underbrace{M \times M \times \cdots \times M}_{N \text{ times}}$$ 4. For example, if $M=2$ and $N=3$, then: $$2^3 = 2 \times 2 \times 2 = 8$$ 5. If $N=0$, by definition: $$M^0 = 1 \text{ if } M \neq 0$$ 6. If $N$ is negative, then: $$M^{-N} = \frac{1}{M^N}$$ 7. If $N$ is not an integer, exponentiation can be defined using logarithms and exponentials, but that is more advanced. Final answer: $M^N$ represents $M$ multiplied by itself $N$ times when $N$ is a positive integer.