1. The problem is to understand and calculate exponents of integers. 2. The general formula for exponents is $a^n$, where $a$ is the base (an integer) and $n$ is the exponent (a positive integer). 3. Important rules: - $a^1 = a$ - $a^0 = 1$ for any $a \neq 0$ - $a^{m+n} = a^m \times a^n$ - $a^{m-n} = \frac{a^m}{a^n}$ 4. Example: Calculate $3^4$. 5. Using the formula, $3^4 = 3 \times 3 \times 3 \times 3$. 6. Multiply step-by-step: $3 \times 3 = 9$, then $9 \times 3 = 27$, then $27 \times 3 = 81$. 7. So, $3^4 = 81$. 8. This means raising an integer to an exponent means multiplying the integer by itself as many times as the exponent indicates.