1. **State the problem:** Simplify the expression $$\frac{x^{5/3}}{x^{2}y^{1/3}}$$ using radical format. 2. **Recall the rules:** - When dividing powers with the same base, subtract the exponents: $$\frac{a^{m}}{a^{n}} = a^{m-n}$$. - Express fractional exponents as radicals: $$a^{m/n} = \sqrt[n]{a^{m}}$$. 3. **Simplify the $x$ terms:** $$\frac{x^{5/3}}{x^{2}} = x^{5/3 - 2} = x^{5/3 - 6/3} = x^{-1/3}$$ 4. **Rewrite the expression:** $$\frac{x^{5/3}}{x^{2}y^{1/3}} = \frac{x^{-1/3}}{y^{1/3}} = x^{-1/3} y^{-1/3}$$ 5. **Convert to radical form:** $$x^{-1/3} = \frac{1}{\sqrt[3]{x}}$$ and $$y^{-1/3} = \frac{1}{\sqrt[3]{y}}$$ 6. **Combine the radicals:** $$x^{-1/3} y^{-1/3} = \frac{1}{\sqrt[3]{x} \sqrt[3]{y}} = \frac{1}{\sqrt[3]{xy}}$$ **Final answer:** $$\boxed{\frac{1}{\sqrt[3]{xy}}}$$