## Elementary Algebra

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