1. **State the problem:** We need to find the composite function $f(g(h(x)))$ given the functions: $$f(x) = x^4 + 7, \quad g(x) = x - 9, \quad h(x) = \sqrt{x}$$ 2. **Recall the definition of composite functions:** $$f(g(h(x))) = f\bigl(g(h(x))\bigr)$$ This means we first apply $h$ to $x$, then apply $g$ to the result, and finally apply $f$ to that. 3. **Calculate $h(x)$:** $$h(x) = \sqrt{x}$$ 4. **Calculate $g(h(x))$:** $$g(h(x)) = g(\sqrt{x}) = \sqrt{x} - 9$$ 5. **Calculate $f(g(h(x)))$:** $$f(g(h(x))) = f(\sqrt{x} - 9) = (\sqrt{x} - 9)^4 + 7$$ 6. **Final answer:** $$\boxed{f(g(h(x))) = (\sqrt{x} - 9)^4 + 7}$$ This expression represents the composite function $f(g(h(x)))$ in terms of $x$.