## Precalculus (6th Edition) Blitzer

$|3x|$
RECALL: (i) When $n$ is even, $\sqrt[n]{a^n} = |a|$. (ii) $\dfrac{\sqrt[n]{a}}{\sqrt[n]{b}}=\sqrt[n]{\dfrac{a}{b}}, b\ne0$. (iii) $\dfrac{a^m}{a^n} = a^{m-n}, a\ne0$. Using the properties above, the given expression simplifies to $\sqrt[4]{\dfrac{162x^5}{2x}} \\=\sqrt[4]{81x^{5-1}} \\=\sqrt[4]{81x^4} \\=\sqrt[4]{3^4x^4} \\=\sqrt[4]{(3x)^4} \\=|3x|.$