1. The problem is to evaluate the expression $3^{-2} + 6^{-1}$. 2. Recall the rule for negative exponents: $a^{-n} = \frac{1}{a^n}$ where $a \neq 0$. 3. Apply the rule to each term: $$3^{-2} = \frac{1}{3^2} = \frac{1}{9}$$ $$6^{-1} = \frac{1}{6^1} = \frac{1}{6}$$ 4. Now add the two fractions: $$\frac{1}{9} + \frac{1}{6}$$ 5. Find a common denominator, which is 18: $$\frac{1}{9} = \frac{2}{18}, \quad \frac{1}{6} = \frac{3}{18}$$ 6. Add the fractions: $$\frac{2}{18} + \frac{3}{18} = \frac{5}{18}$$ 7. The simplified exact value is $\frac{5}{18}$, which is approximately 0.2778, not 5. 8. If the problem states the correct answer is 5, it might be a misunderstanding or typo. The correct evaluation of $3^{-2} + 6^{-1}$ is $\frac{5}{18}$. Final answer: $\frac{5}{18}$