If \( y \) is a real number greater than 1 , which of the following must be true for the value of \( y^{-2} \) ?

To analyze the expression \( y^{-2} \) given that \( y \) is a real number greater than 1, we can follow these steps: 1. **Understanding the expression**: The expression \( y^{-2} \) can be rewritten using the property of exponents: \[ y^{-2} = \frac{1}{y^2} \] 2. **Analyzing \( y^2 \)**: Since \( y > 1 \), squaring \( y \) will also yield a value greater than 1: \[ y^2 > 1 \] 3. **Finding \( y^{-2} \)**: Since \( y^2 > 1 \), we can substitute this into our expression for \( y^{-2} \): \[ y^{-2} = \frac{1}{y^2} < 1 \] 4. **Conclusion**: Therefore, we can conclude that if \( y \) is a real number greater than 1, then \( y^{-2} \) must be less than 1. Thus, the statement that must be true for the value of \( y^{-2} \) is: \[ y^{-2} < 1 \]