https://file.aiquickdraw.com/mathbot/file/17270950456650tjmg07u.jpg

The image shows the equation:

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

Let’s verify both sides:

### Left Side:
\[
2^{-1} = \frac{1}{2}
\]
\[
3^{-2} = \left(\frac{1}{3}\right)^2 = \frac{1}{9}
\]
So,
\[
2^{-1} + 3^{-2} = \frac{1}{2} + \frac{1}{9}
\]
We need a common denominator:
\[
\frac{1}{2} + \frac{1}{9} = \frac{9}{18} + \frac{2}{18} = \frac{11}{18}
\]

### Right Side:
\[
\frac{1}{2} + \frac{2}{3}
\]
Again, we find a common denominator:
\[
\frac{1}{2} + \frac{2}{3} = \frac{3}{6} + \frac{4}{6} = \frac{7}{6}
\]

### Conclusion:
\[
\frac{11}{18} \neq \frac{7}{6}
\]

So, the equation given is **not true**. The left and right sides are not equal.

Would you like more details or have any questions?

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Here are 5 related questions:

1. What are negative exponents and how do they work?
2. How can we find common denominators when adding fractions?
3. How do we simplify expressions with fractional exponents?
4. What is the rule for comparing fractions with different denominators?
5. Can equations involving exponents have multiple solutions?

**Tip:** When dealing with exponents, especially negative ones, remember that they represent reciprocals or inverse powers.

Learn how to verify the equation 2^(-1) + 3^(-2) = 1/2 + 2/3 by simplifying both sides. This problem covers negative exponents and adding fractions with different denominators, suitable for students in Grades 7-9.

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