1. The problem is to evaluate $$\left(\frac{81}{16}\right)^{\frac{1}{4}} + \left(\frac{81}{16}\right)^0$$. 2. Recall the rules: - Any number raised to the power 0 is 1, so $$a^0 = 1$$ for any $$a \neq 0$$. - The fourth root of a number is the same as raising it to the power $$\frac{1}{4}$$. 3. Evaluate $$\left(\frac{81}{16}\right)^0$$: $$\left(\frac{81}{16}\right)^0 = 1$$. 4. Evaluate $$\left(\frac{81}{16}\right)^{\frac{1}{4}}$$: Since $$\frac{81}{16} = \frac{3^4}{2^4}$$, we have $$\left(\frac{81}{16}\right)^{\frac{1}{4}} = \left(\frac{3^4}{2^4}\right)^{\frac{1}{4}} = \frac{3^{4 \times \frac{1}{4}}}{2^{4 \times \frac{1}{4}}} = \frac{3^1}{2^1} = \frac{3}{2}$$. 5. Add the two results: $$\frac{3}{2} + 1 = \frac{3}{2} + \frac{2}{2} = \frac{5}{2}$$. 6. Final answer: $$\boxed{\frac{5}{2}}$$.