Use properties of logarithms to find the exact value of the expression. Do not use a calculator. \[ \log _{16} 2+\log _{16} 8 \]

To find the exact value of the expression \(\log_{16} 2 + \log_{16} 8\) using properties of logarithms, follow these steps: 1. **Use the Product Property of Logarithms**: The product property states that \(\log_b (M) + \log_b (N) = \log_b (MN)\). Applying this property: \[ \log_{16} 2 + \log_{16} 8 = \log_{16} (2 \times 8) = \log_{16} 16 \] 2. **Evaluate the Logarithm**: Since \(16\) is the base of the logarithm, \(\log_{16} 16\) asks, "To what power must \(16\) be raised to get \(16\)?" The answer is \(1\): \[ \log_{16} 16 = 1 \] Therefore, the exact value of the expression is: **Answer:** \(1\)