Answer:
[tex]\large\boxed{\sqrt{126x^{11}}=3x^5\sqrt{14x}}[/tex]
Step-by-step explanation:
[tex]Domain:\ x\geq0\\\\\sqrt{126x^{11}}=\sqrt{9\cdot14\cdot x^{10+1}}\\\\\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=\sqrt{9\cdot14\cdot x^{10}\cdot x^1}=\sqrt{9\cdot14\cdot x^{5\cdot2}\cdot x}\\\\\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\ \text{and}\ (a^n)^m=a^{nm}\\\\=\sqrt9\cdot\sqrt{14}\cdot\sqrt{(x^5)^2}\cdot\sqrt{x}\\\\\text{use}\ \sqrt{a^2}=a\ \text{for}\ a\geq0\\\\=3\cdot\sqrt{14}\cdot x^5\cdot\sqrt{x}=3x^5\sqrt{14x}[/tex]
