To simplify the expression $3x^{-2}$, let's follow these steps:

Step 1: Identify the base of the exponential term

In the expression $3x^{-2}$, the base of the exponential term is $x$, and the exponent is $-2$.

Step 2: Apply the rule for negative exponents

The rule for negative exponents is:

$a^{-n} = \frac{1}{a^n}$

Using this rule, we can rewrite $x^{-2}$ as:

$x^{-2} = \frac{1}{x^2}$

Step 3: Simplify the expression

Now, substitute this into the original expression:

$3x^{-2} = 3 \times \frac{1}{x^2} = \frac{3}{x^2}$

Final simplified expression:

$\frac{3}{x^2}$

Would you like more details or have any questions about this simplification?

Here are some related questions for you:

1. What happens when the exponent is a positive integer instead of negative?
2. How do you handle fractional exponents in expressions like $x^{\frac{1}{2}}$?
3. Can you simplify expressions with both positive and negative exponents?
4. How would you simplify $4x^{-3}$ using the same process?
5. What are the rules for exponents when multiplying two terms with the same base?

Tip: Remember, negative exponents are a way of representing division.