To simplify the expression [tex]\(\sqrt{400 x^{100}}\)[/tex], let's proceed step-by-step.
1. Simplify the square root of the constants:
- [tex]\(\sqrt{400}\)[/tex]:
[tex]\[
\sqrt{400} = \sqrt{20^2} = 20
\][/tex]
2. Simplify the square root of the variables:
- [tex]\(\sqrt{x^{100}}\)[/tex]:
[tex]\[
\sqrt{x^{100}} = x^{\frac{100}{2}} = x^{50}
\][/tex]
3. Combine both simplified parts:
- Combining the results from the previous steps, we have:
[tex]\[
\sqrt{400 x^{100}} = 20 \cdot x^{50} = 20 x^{50}
\][/tex]
Thus, the simplified form of [tex]\(\sqrt{400 x^{100}}\)[/tex] is:
[tex]\[
20 x^{50}
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{20 x^{50}}
\][/tex]
