Answer
$\dfrac{\sqrt[6]{7,776}}{6}$
Work Step by Step
Using $\sqrt[n]{x^m}=x^{\frac{m}{n}},$ the given expression, $
\dfrac{\sqrt[]{6}}{\sqrt[3]{36}}
,$ is equivalent to
\begin{align*}
&
\dfrac{\sqrt[]{6}}{\sqrt[3]{6^2}}
\\\\&=
\dfrac{6^{\frac{1}{2}}}{6^{\frac{2}{3}}}
.\end{align*}
Using the laws of exponents, the expression above is equivalent to
\begin{align*}
&
6^{\frac{1}{2}-\frac{2}{3}}
&\left( \text{use }\dfrac{a^{x}}{a^y}=a^{x-y} \right)
\\\\&=
6^{\frac{3}{6}-\frac{4}{6}}
\\\\&=
6^{-\frac{1}{6}}
\\\\&=
\dfrac{1}{6^{\frac{1}{6}}}
&\left( \text{use }a^{-x}=\dfrac{1}{a^x} \right)
\\\\&=
\dfrac{1}{\sqrt[6]{6^1}}
\\\\&=
\dfrac{1}{\sqrt[6]{6}}
\\\\&=
\dfrac{1}{\sqrt[6]{6}}\cdot\dfrac{\sqrt[6]{6^5}}{\sqrt[6]{6^5}}
&\left( \text{rationalize denominator} \right)
\\\\&=
\dfrac{\sqrt[6]{6^5}}{\sqrt[6]{6^6}}
\\\\&=
\dfrac{\sqrt[6]{7,776}}{6}
.\end{align*}
Hence, the simplified form of the given expression is $
\dfrac{\sqrt[6]{7,776}}{6}
.$
