$$ \leftarrow \begin{array}{l} ext { Simplify. } \ 3^{-4} \cdot 3^{6} \ 3^{-4} \cdot 3^{6}=\square\end{array} $$

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$$ \leftarrow \begin{array}{l}	ext { Simplify. } \ 3^{-4} \cdot 3^{6} \ 3^{-4} \cdot 3^{6}=\square\end{array} $$

UpStudy AI · Accepted Answer

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:** $$ 3^{-4} \cdot 3^{6} = 9 $$
$$ 3^{-4} \cdot 3^{6} = 9 $$

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