1. The problem is to simplify the expression \(\sqrt{\sqrt{x}}\). 2. Recall the rule for radicals: \(\sqrt{a} = a^{\frac{1}{2}}\). 3. Applying this rule, \(\sqrt{\sqrt{x}} = \sqrt{x^{\frac{1}{2}}}\). 4. Using the rule again, \(\sqrt{x^{\frac{1}{2}}} = \left(x^{\frac{1}{2}}\right)^{\frac{1}{2}}\). 5. When raising a power to another power, multiply the exponents: \(x^{\frac{1}{2} \times \frac{1}{2}} = x^{\frac{1}{4}}\). 6. Therefore, \(\sqrt{\sqrt{x}} = x^{\frac{1}{4}}\). 7. In simpler terms, the fourth root of \(x\) is the same as the square root of the square root of \(x\).