Exponent Definition
1. The problem is to understand what an exponent is.
2. An exponent refers to the number that indicates how many times a base is multiplied by itself.
3. For example, in the expression $a^n$, $a$ is the base and $n$ is the exponent.
4. If $n$ is a positive integer, $a^n$ means multiplying $a$ by itself $n$ times: $$a^n = \underbrace{a \times a \times \cdots \times a}_{n\text{ times}}.$$
5. For instance, $3^4 = 3 \times 3 \times 3 \times 3 = 81$.
6. Exponents can also be zero or negative, where $a^0 = 1$ if $a \neq 0$, and $a^{-n} = \frac{1}{a^n}$ for positive $n$.
7. In summary, an exponent tells you how many times to use the base in a multiplication.