remember [tex] \sqrt[n]{x^m} =x^ \frac{m}{n} [/tex] and
[tex](x^m)(x^n)=x^{m+n}[/tex] and
[tex] \frac{x^m}{x^n}=x^{m-n} [/tex] and
[tex](x^m)^n=x^{mn}[/tex]
so
[tex]( \sqrt[4]{9})( \frac{ \sqrt{9} }{\sqrt[4]{9^5}}) [/tex]=
[tex]( \sqrt[4]{9})( \frac{ \sqrt{2}{3^2} }{9^\frac{5}{4}}) [/tex]=
[tex]( \sqrt[4]{9})( 3^\frac{2}{2} }{9\sqrt[4]{9}}) [/tex]=
[tex] \frac{3}{9} [/tex]=
[tex] \frac{1}{3} [/tex]
