$\frac{{\sqrt {\frac{2}{3}}  - \sqrt {\frac{3}{2}} }}{{\sqrt {24} }} \times \frac{{\sqrt[3]{{27}}}}{{{2^{ - 3}}}} =  - \frac{1}{{12}} \times 24 =  - 2$

$1 \to \frac{{\sqrt 2  \times \sqrt 2 }}{{\sqrt 2  \times \sqrt 2 }} - \frac{{\sqrt 3  \times \sqrt 3 }}{{\sqrt 2  \times \sqrt 3 }} = \frac{{2 - 3}}{{\sqrt 6 }} =  - \frac{2}{{\sqrt 6 }}$

$2 \to \frac{{ - \frac{1}{{\sqrt 6 }}}}{{\frac{{\sqrt {24} }}{1}}} =  - \frac{1}{{\sqrt {6 \times 24} }} =  - \frac{1}{{6 \times 2}} =  - \frac{1}{{12}}$

$3 \to \frac{{\sqrt[3]{{27}}}}{{2 - 3}} = \frac{{\sqrt[3]{{{4^3}}}}}{{{2^{ - 3}}}} = \frac{3}{{{{(\frac{1}{2})}^3}}} = \frac{{\frac{3}{1}}}{{\frac{1}{8}}} = 24$

توجه داشته باشید:

$\begin{gathered}
  \sqrt[n]{a} \times \sqrt[n]{b} = \sqrt[n]{{ab}} \hfill \\
  \sqrt[n]{{\frac{a}{b}}} = \frac{{\sqrt[n]{a}}}{{\sqrt[n]{b}}} \hfill \\
  {a^{ - n}} = {(\frac{1}{a})^n} \hfill \\ 
\end{gathered} $