Answer
$|3x|$
Work Step by Step
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
$\sqrt[4]{\dfrac{162x^5}{2x}}
\\=\sqrt[4]{81x^{5-1}}
\\=\sqrt[4]{81x^4}
\\=\sqrt[4]{3^4x^4}
\\=\sqrt[4]{(3x)^4}
\\=|3x|.$
