1. **State the problem:** Calculate the value of $$\sqrt[3]{81} + 8^{\frac{1}{3}}$$. 2. **Recall the cube root and exponent rules:** The cube root of a number $a$ is the same as $a^{\frac{1}{3}}$. 3. **Rewrite the expression using exponents:** $$81^{\frac{1}{3}} + 8^{\frac{1}{3}}$$. 4. **Simplify each term:** - $81 = 3^4$, so $$81^{\frac{1}{3}} = (3^4)^{\frac{1}{3}} = 3^{\frac{4}{3}} = 3^{1 + \frac{1}{3}} = 3 \times 3^{\frac{1}{3}}$$. - $8 = 2^3$, so $$8^{\frac{1}{3}} = (2^3)^{\frac{1}{3}} = 2^{3 \times \frac{1}{3}} = 2^1 = 2$$. 5. **Evaluate the cube root of 3:** $$3^{\frac{1}{3}} = \sqrt[3]{3}$$ (approximate value if needed). 6. **Combine the terms:** $$3 \times \sqrt[3]{3} + 2$$. 7. **Final answer:** $$3 \sqrt[3]{3} + 2$$. This is the simplified exact form of the expression.