1. We are asked to simplify the expression $$\sqrt[8]{(a-4)^4}$$. 2. Recall the rule for radicals and exponents: $$\sqrt[n]{x^m} = x^{\frac{m}{n}}$$. 3. Applying this rule, we rewrite the expression as $$\left(a-4\right)^{\frac{4}{8}}$$. 4. Simplify the fraction $$\frac{4}{8} = \frac{1}{2}$$. 5. So the expression becomes $$\left(a-4\right)^{\frac{1}{2}}$$. 6. The exponent $$\frac{1}{2}$$ means the square root, so $$\left(a-4\right)^{\frac{1}{2}} = \sqrt{a-4}$$. 7. Therefore, the simplified form of $$\sqrt[8]{(a-4)^4}$$ is $$\sqrt{a-4}$$.