To solve \( 3^{-1} + 2^{-2} \):

1. \( 3^{-1} \) means the reciprocal of 3, which is \( \frac{1}{3} \).
2. \( 2^{-2} \) means the reciprocal of \( 2^2 \), which is \( \frac{1}{4} \).

Now, let's add them:

\[
3^{-1} + 2^{-2} = \frac{1}{3} + \frac{1}{4}
\]

To add these fractions, find a common denominator. The least common denominator (LCD) of 3 and 4 is 12.

\[
\frac{1}{3} = \frac{4}{12}, \quad \frac{1}{4} = \frac{3}{12}
\]

Now add:

\[
\frac{4}{12} + \frac{3}{12} = \frac{7}{12}
\]

So, the result is \( \frac{7}{12} \).

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you find the reciprocal of a number?
2. What is the process for adding fractions with different denominators?
3. How do you simplify expressions with negative exponents?
4. What are common denominators, and how do you find them?
5. How do negative exponents affect powers of a number?

**Tip:** When dealing with negative exponents, always remember that they represent the reciprocal of the positive exponent value.

Learn how to solve the expression 3^{-1} + 2^{-2} by applying negative exponents and adding fractions. This step-by-step guide covers important concepts like reciprocals, exponent rules, and fraction addition. Suitable for students in Grades 6-8.

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