Simplify the Nested Radical: 10th Root of Square Root of x^20

To solve the problem, we'll simplify $\sqrt[10]{\sqrt{x^{20}}}$ using properties of exponents and roots:

• Step 1: Convert each part into exponent form. We have $\sqrt{x^{20}}$, which can be rewritten as $(x^{20})^{1/2}$.
• Step 2: Simplify the expression $(x^{20})^{1/2}$. Using the power of a power property, this becomes $x^{20 \cdot (1/2)} = x^{10}$.
• Step 3: Apply the 10th root to the simplified result: $\sqrt[10]{x^{10}}$, which can be written as $(x^{10})^{1/10}$.
• Step 4: Simplify $(x^{10})^{1/10}$ using the power of a power property again, we get $x^{(10 \cdot (1/10))} = x^1 = x$.

Therefore, the expression simplifies to $x$.

Conclusion: The solution to the problem is $x$.