The expression as a rational exponent is [tex]x^{\frac{2}{12} }y^{\frac{9}{12}[/tex]
Given the indices;
[tex]\sqrt[6]{x} \times \sqrt[4]{y^3}[/tex]
According to the laws of indices
[tex]\sqrt[n]{x} = x^{\frac{1}{n} }[/tex]
Applying this to solve the given question will give;
[tex]\sqrt[6]{x} \times \sqrt[4]{y^3}\\= x^{\frac{1}{6} }\times y^{\frac{3}{4}} \\= (x^{\frac{1}{6} }) ^{\frac{2}{2} } (\times y^{\frac{3}{4}})^{\frac{3}{3} } \\\\=x^{\frac{2}{12} }y^{\frac{9}{12} }[/tex]
Hence the expression as a rational exponent is [tex]x^{\frac{2}{12} }y^{\frac{9}{12}[/tex]
Learn more on indices here; https://brainly.com/question/8952483
