https://file.aiquickdraw.com/mathbot/file/1727065414960d8rbyslw.jpg

The image contains the mathematical expression:

\[
3^{-1} + 4^{-1}
\]

This can be simplified using the properties of negative exponents, which state that \( a^{-1} = \frac{1}{a} \). Applying this:

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

Now, summing the fractions:

\[
\frac{1}{3} + \frac{1}{4} = \frac{4}{12} + \frac{3}{12} = \frac{7}{12}
\]

Thus, the result of the expression is:

\[
\frac{7}{12}
\]

Would you like further details or have any questions?

Here are 5 related questions to explore:
1. How do you simplify fractions with different denominators?
2. What is the general rule for simplifying negative exponents?
3. How can this concept apply to more complex expressions?
4. What is the decimal equivalent of \(\frac{7}{12}\)?
5. How do you handle negative exponents in larger algebraic expressions?

**Tip:** Remember, when working with fractions, always look for a common denominator to simplify the sum.

Learn how to solve the mathematical expression 3^{-1} + 4^{-1} using the concept of negative exponents and fractions. This problem teaches key concepts such as simplifying negative exponents and finding a common denominator for fractions. Suitable for students in Grades 7-9.

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