1. Stating the problem: Simplify the expression $$\sqrt[n]{x}\sqrt[n]{x}\sqrt[n]{x}\sqrt[n]{x}$$. 2. Recall the property of radicals: $$\sqrt[n]{a}\cdot\sqrt[n]{b} = \sqrt[n]{ab}$$. 3. Use this property step-by-step: $$\sqrt[n]{x}\sqrt[n]{x} = \sqrt[n]{x \cdot x} = \sqrt[n]{x^2}$$. 4. Similarly, multiply all four terms: $$\sqrt[n]{x}\sqrt[n]{x}\sqrt[n]{x}\sqrt[n]{x} = \sqrt[n]{x^2} \cdot \sqrt[n]{x^2} = \sqrt[n]{x^2 \cdot x^2} = \sqrt[n]{x^4}$$. 5. Using the radical exponent property, $$\sqrt[n]{x^4} = x^{\frac{4}{n}}$$. 6. Final answer: $$\sqrt[n]{x}\sqrt[n]{x}\sqrt[n]{x}\sqrt[n]{x} = x^{\frac{4}{n}}$$.