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Convert them to exponents and then divide. \[\sqrt[n]{a} = a^{1/n}\]

So for example \[\sqrt[4]{x^3}\text{ divided by }\sqrt[3]{x^2} \] would be \[\frac{x^{\frac{3}{4}}}{x^{\frac{2}{3}}}\] or \[x^{\frac{3}{4}-\frac{2}{3}}\]

Which would then be \[x^{\frac{1}{12}}=\sqrt[12]{x}\]

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