Answer:
[tex]\large\boxed{\sqrt{84x^7}=2x^3\sqrt{21x}}[/tex]
Step-by-step explanation:
[tex]Domain:\ x\geq0\\\\\sqrt{84x^7}=\sqrt{4\cdot21\cdot x^{6+1}}\\\\\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=\sqrt{4\cdot21\cdot x^6\cdot x^1}\\\\\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\sqrt4\cdot\sqrt{21}\cdot\sqrt{x^{3\cdot2}}\cdot\sqrt{x}\\\\\text{use}\ (a^n)^m=a^{nm}\\\\=2\cdot\sqrt{21}\cdot\sqrt{(x^3)^2}\cdot\sqrt{x}\\\\\text{use}\ \sqrt{a^2}=a\ \text{for}\ a\geq0\\\\=2\cdot\sqrt{21}\cdot x^3\cdot\sqrt{x}=2x^3\sqrt{21x}[/tex]
