Question
\begin{tabular}{l} implify the expression. Write your answer as an integer or simplified fraction. \\ \( 3^{-2}+6^{-1}=\square \) \\ \hline\( \square \) \\ \hline\end{tabular}
Ask by Long Warren. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The simplified expression is \(\frac{5}{18}\) or approximately \(0.2777\).
Solution
Calculate or simplify the expression \( 3^{-2}+6^{-1} \).
Calculate the value by following steps:
- step0: Calculate:
\(3^{-2}+6^{-1}\)
- step1: Evaluate the power:
\(\frac{1}{9}+6^{-1}\)
- step2: Calculate:
\(\frac{1}{9}+\frac{1}{6}\)
- step3: Reduce fractions to a common denominator:
\(\frac{2}{9\times 2}+\frac{3}{6\times 3}\)
- step4: Multiply the numbers:
\(\frac{2}{18}+\frac{3}{6\times 3}\)
- step5: Multiply the numbers:
\(\frac{2}{18}+\frac{3}{18}\)
- step6: Transform the expression:
\(\frac{2+3}{18}\)
- step7: Add the numbers:
\(\frac{5}{18}\)
The simplified form of the expression \(3^{-2}+6^{-1}\) is \(\frac{5}{18}\) or \(0.2777...\)
Reviewed and approved by the UpStudy tutoring team
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Explain 
Simplify this solution Beyond the Answer
To simplify the expression \(3^{-2} + 6^{-1}\), we first evaluate each term. Starting with \(3^{-2}\), this is equal to \(\frac{1}{3^2} = \frac{1}{9}\). Next, for \(6^{-1}\), this simplifies to \(\frac{1}{6}\). Now, to combine these two fractions, we need a common denominator. The least common multiple of \(9\) and \(6\) is \(18\). Rewriting \(\frac{1}{9}\) as \(\frac{2}{18}\) and \(\frac{1}{6}\) as \(\frac{3}{18}\), we can now add them: \[ \frac{2}{18} + \frac{3}{18} = \frac{5}{18}. \] So, the final answer is: \(\frac{5}{18}\).
