\( 1 \quad 5.5 ^ { x - 1 } \cdot ( 25 ^ { 1 - x } ) ^ { 0 } \)

Let's simplify the given expression: \[ 1 \quad 5.5^{x - 1} \cdot \left(25^{1 - x}\right)^0 \] ### Step-by-Step Simplification: 1. **Understanding the Components:** - The expression consists of three parts multiplied together: \(1\), \(5.5^{x - 1}\), and \(\left(25^{1 - x}\right)^0\). 2. **Simplifying \(\left(25^{1 - x}\right)^0\):** - Any non-zero number raised to the power of \(0\) is \(1\). - Therefore, \(\left(25^{1 - x}\right)^0 = 1\). 3. **Substituting Back:** - Now, the expression becomes: \[ 1 \cdot 5.5^{x - 1} \cdot 1 \] - Multiplying by \(1\) doesn't change the value, so: \[ 5.5^{x - 1} \] ### Final Simplified Expression: \[ 5.5^{x - 1} \] ### Additional Insights (Optional): - **Expressing with Base \(5.5\):** - The expression \(5.5^{x - 1}\) can also be written as: \[ \frac{5.5^x}{5.5} \] - **Alternative Bases:** - If needed, \(5.5\) can be expressed as \(\frac{11}{2}\), but unless there's a specific reason to change the base, it's simplest to leave the expression as is. ### Conclusion: The original expression simplifies neatly to: \[ 5.5^{x - 1} \]