[tex]3\sqrt{32x^4z}=3\sqrt{32}\cdot\sqrt{x^4}\cdot\sqrt{z}=3\sqrt{16\cdot2}\cdot\sqrt{(x^2)^2}\cdot\sqrt{z}\\\\=3\sqrt{16}\cdot\sqrt2\cdot x^2\cdot\sqrt{z}=3\cdot4\cdot\sqrt{2}\cdot x^2\cdot\sqrt{z}\\\\=12x^2\sqrt{2z}\\\\\text{Used:}\\\\\sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b}\\\\\sqrt{a^2}=a\\\\(a^n)^m=a^{n\cdot m}[/tex]
