1. The problem is to simplify the expression $\sqrt[4]{25x^4}$.\n\n2. Recall the rule for fourth roots: $\sqrt[4]{a^4} = a$ if $a \geq 0$. Also, $\sqrt[4]{ab} = \sqrt[4]{a} \times \sqrt[4]{b}$.\n\n3. Apply the rule to separate the root: $$\sqrt[4]{25x^4} = \sqrt[4]{25} \times \sqrt[4]{x^4}.$$\n\n4. Simplify each part: $\sqrt[4]{25} = \sqrt[4]{5^2} = 5^{\frac{2}{4}} = 5^{\frac{1}{2}} = \sqrt{5}$.\n\n5. For $\sqrt[4]{x^4}$, since the root and the power are the same, this simplifies to $|x|$.\n\n6. Therefore, the simplified expression is $$\sqrt{5} \times |x| = |x|\sqrt{5}.$$\n\nFinal answer: $|x|\sqrt{5}$.