[tex]\sqrt[4]{x^{6}} = x^{\frac{6}{4}} = x^{\frac{3}{2}}[/tex]
[tex]\sqrt[12]{x^{9}}= x^{\frac{9}{12}} = x^{\frac{3}{4}}[/tex]
[tex]\sqrt[4]{x^{6}} \cdot \sqrt[12]{x^{9}} = x^{\frac{3}{2}} \cdot x^{\frac{3}{4}}[/tex]
[tex]= x^{\frac{3}{2} + \frac{3}{4}}[/tex]
[tex]= x^{\frac{6 + 3}{4}}[/tex]
[tex]= x^{\frac{9}{4}}[/tex]
