Answer
$2x^{\frac{1}{6}}$
Work Step by Step
We will use the rule $\frac{a^{m}}{a^{n}}=a^{m-n}$ in the simplification of the expression:
$\frac{18x^{\frac{1}{2}}}{9x^{\frac{1}{3}}}$
$=\frac{18}{9}\times\frac{x^{\frac{1}{2}}}{x^{\frac{1}{3}}}$
$=2\times x^{\frac{1}{2}-(\frac{1}{3})}$
$=2\times x^{\frac{3-2}{6}}$
$=2x^{\frac{1}{6}}$
