To evaluate the equation \((3^{-5} \cdot (\sqrt[4]{81})^3) / (3^{-4}) = 3^{-6}\), let's simplify the left side step by step.
1. **Simplify \(\sqrt[4]{81}\)**:
\[
81 = 3^4 \implies \sqrt[4]{81} = \sqrt[4]{3^4} = 3
\]
So, \((\sqrt[4]{81})^3 = 3^3 = 27\).
2. **Substitute into the equation**:
\[
3^{-5} \cdot (3^3) / (3^{-4}) = 3^{-5} \cdot 27 / 3^{-4}
\]
3. **Convert 27 to a power of 3**:
\[
27 = 3^3
\]
So the expression becomes:
\[
3^{-5} \cdot 3^3 / 3^{-4}
\]
4. **Combine using the Product Property**:
\[
3^{-5 + 3} / 3^{-4} = 3^{-2} / 3^{-4}
\]
5. **Apply the Quotient Property**:
\[
3^{-2 - (-4)} = 3^{-2 + 4} = 3^2
\]
The left side simplifies to:
\[
3^2
\]
Now compare that to the right side \(3^{-6}\):
Since \(3^2 \neq 3^{-6}\), the original equation is false.
**Final Answer**: **False. There is an error in calculation using the Quotient Property.**