Simplify: \( w \cdot w^{7} \cdot w^{-9} \)

To simplify the expression \( w \cdot w^{7} \cdot w^{-9} \), you can use the **laws of exponents**, specifically the **product of powers** rule. Here's how it works step-by-step: 1. **Combine the exponents:** When you multiply terms with the same base, you add their exponents. \[ w \cdot w^{7} \cdot w^{-9} = w^{1} \cdot w^{7} \cdot w^{-9} \] 2. **Add the exponents:** \[ w^{1 + 7 - 9} = w^{-1} \] 3. **Simplify the negative exponent:** A negative exponent indicates the reciprocal of the base raised to the positive exponent. \[ w^{-1} = \frac{1}{w} \] **Final Answer:** \[ \frac{1}{w} \]