Answer
$\frac{1}{x^{\frac{13}{2}}}$
Work Step by Step
$\frac{(x^{\frac{2}{3}}x^{-3})^{3}}{x^{-\frac{1}{2}}}$
=$\frac{(x^{\frac{2}{3}-3})^{3}}{x^{-\frac{1}{2}}}$
=$\frac{(x^{\frac{2-3(3)}{3}})^{3}}{x^{-\frac{1}{2}}}$
=$\frac{(x^{\frac{2-9}{3}})^{3}}{x^{-\frac{1}{2}}}$
=$\frac{(x^{\frac{-7}{3}})^{3}}{x^{-\frac{1}{2}}}$
=$\frac{(x^{-\frac{7}{3}\times3})}{x^{-\frac{1}{2}}}$
=$\frac{x^{-7}}{x^{-\frac{1}{2}}}$
=$\frac{1}{x^{-\frac{1}{2}+7}}$
=$\frac{1}{x^{\frac{-1+14}{2}}}$
=$\frac{1}{x^{\frac{13}{2}}}$
