1. **Problem:** Find the value of $$\sqrt[4]{81}^{-2}$$. 2. **Formula and rules:** - The fourth root of a number $$a$$ is $$a^{\frac{1}{4}}$$. - Negative exponents mean reciprocal: $$a^{-n} = \frac{1}{a^n}$$. 3. **Step-by-step solution:** - Express 81 as a power of 3: $$81 = 3^4$$. - Then $$\sqrt[4]{81} = 81^{\frac{1}{4}} = (3^4)^{\frac{1}{4}} = 3^{4 \times \frac{1}{4}} = 3^1 = 3$$. - Now raise to the power $$-2$$: $$\left(3\right)^{-2} = \frac{1}{3^2} = \frac{1}{9}$$. 4. **Answer:** The value is $$\frac{1}{9}$$.