It seems like you're asking to compute the expression involving powers with negative exponents:

$3^{-2} - 2^{-1}$

Step-by-Step Solution:

1. Evaluate $3^{-2}$: $3^{-2} = \frac{1}{3^2} = \frac{1}{9}$

2. Evaluate $2^{-1}$: $2^{-1} = \frac{1}{2}$

3. Subtract the two results: $\frac{1}{9} - \frac{1}{2}$

4. To subtract these fractions, find a common denominator. The least common denominator (LCD) of 9 and 2 is 18.

   Convert both fractions: $\frac{1}{9} = \frac{2}{18}, \quad \frac{1}{2} = \frac{9}{18}$

5. Now subtract: $\frac{2}{18} - \frac{9}{18} = \frac{-7}{18}$

Final Answer:

$3^{-2} - 2^{-1} = \frac{-7}{18}$

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Would you like more details on any part of the solution?

Here are some related questions:

1. How do you handle negative exponents when dealing with larger numbers?
2. What happens when you raise a number to the power of 0?
3. How can I add or subtract fractions with different denominators?
4. What is the rule for multiplying numbers with negative exponents?
5. How do I simplify expressions with both positive and negative exponents?

Tip: Always remember that a negative exponent means to take the reciprocal of the base raised to the positive exponent.