Questions: Simplify the expression. Write your answer as an integer or simplified fraction. 3^-2+6^-1=

Solution Steps

To simplify the expression \(3^{-2} + 6^{-1}\), we need to evaluate each term separately. The term \(3^{-2}\) is the reciprocal of \(3^2\), and \(6^{-1}\) is the reciprocal of \(6\). After calculating these values, we add them together to get the final result.

We start by calculating \(3^{-2}\): \[ 3^{-2} = \frac{1}{3^2} = \frac{1}{9} \approx 0.1111 \]

Next, we calculate \(6^{-1}\): \[ 6^{-1} = \frac{1}{6} \approx 0.1667 \]

Now, we add the two results together: \[ 3^{-2} + 6^{-1} = \frac{1}{9} + \frac{1}{6} \] To add these fractions, we find a common denominator, which is 18: \[ \frac{1}{9} = \frac{2}{18}, \quad \frac{1}{6} = \frac{3}{18} \] Thus, \[ \frac{1}{9} + \frac{1}{6} = \frac{2}{18} + \frac{3}{18} = \frac{5}{18} \approx 0.2778 \]

Final Answer