+118723 Your question needs brackets to make it unambiguous.
Is this is what you have asked.
$$15x^{1/2}y^{1/12}/(24x^{5/6}y^{1/6})\\\\
=\frac{15}{24}x^{1/2-5/6}y^{1/12-1/6}\\\\
=\frac{5}{8}x^{3/6-5/6}y^{1/12-2/12}\\\\
=\frac{5}{8}x^{-2/6}y^{-1/12}\\\\
=\frac{5}{8y^{1/3}y^{1/12}}$$
+118723 Your question needs brackets to make it unambiguous.
Is this is what you have asked.
$$15x^{1/2}y^{1/12}/(24x^{5/6}y^{1/6})\\\\
=\frac{15}{24}x^{1/2-5/6}y^{1/12-1/6}\\\\
=\frac{5}{8}x^{3/6-5/6}y^{1/12-2/12}\\\\
=\frac{5}{8}x^{-2/6}y^{-1/12}\\\\
=\frac{5}{8y^{1/3}y^{1/12}}$$
