Answer
$\dfrac{1}{x^{13/2}}$
Work Step by Step
Using laws of exponents, the expression $
\dfrac{(x^{2/3}x^{-3})^3}{x^{-1/2}}
$ simplifies to
\begin{array}{l}
\dfrac{x^{\frac{2}{3}\cdot3}x^{-3(3)}}{x^{-\frac{1}{2}}}
\\\\=
\dfrac{x^{2}x^{-9}}{x^{-\frac{1}{2}}}
\\\\=
x^{2+(-9)-\left( -\frac{1}{2} \right)}
\\\\=
x^{\frac{4-18+1}{2}}
\\\\=
x^{\frac{-13}{2}}
\\\\=
\dfrac{1}{x^{13/2}}
.\end{array}
