\( \leftarrow \begin{array}{l}\text { Simplify. } \\ 3^{-4} \cdot 3^{6} \\ 3^{-4} \cdot 3^{6}=\square\end{array} \)

To simplify the expression \( 3^{-4} \cdot 3^{6} \), you can use the **laws of exponents**, specifically the **Product of Powers** rule. Here's a step-by-step breakdown: 1. **Identify the Rule:** When multiplying two exponents with the same base, you add the exponents. \[ a^m \cdot a^n = a^{m+n} \] 2. **Apply the Rule to the Given Expression:** \[ 3^{-4} \cdot 3^{6} = 3^{-4 + 6} \] 3. **Perform the Addition in the Exponent:** \[ -4 + 6 = 2 \] So, \[ 3^{-4} \cdot 3^{6} = 3^{2} \] 4. **Simplify the Final Expression:** \[ 3^{2} = 9 \] Therefore, \[ 3^{-4} \cdot 3^{6} = 9 \] **Answer:** \( 3^{-4} \cdot 3^{6} = 9 \)