1. The problem asks to find an expression equivalent to $$\sqrt[4]{x^2 + 8x + 16}$$ where $$x > 0$$. 2. First, recognize that the expression inside the fourth root is a quadratic: $$x^2 + 8x + 16$$. 3. Factor the quadratic: $$x^2 + 8x + 16 = (x + 4)^2$$ because $$4 \times 4 = 16$$ and $$4 + 4 = 8$$. 4. Substitute back into the original expression: $$\sqrt[4]{(x + 4)^2}$$. 5. Use the property of radicals: $$\sqrt[n]{a^m} = a^{m/n}$$, so $$\sqrt[4]{(x + 4)^2} = (x + 4)^{2/4} = (x + 4)^{1/2}$$. 6. Since $$x > 0$$, $$x + 4 > 0$$, so the expression is valid and simplifies to $$ (x + 4)^{1/2} $$. 7. Therefore, the equivalent expression is option D: $$(x + 4)^{1/2}$$.