use exponential propoerties to make your life easier
remember
[tex](x^m)^n=x^{mn}[/tex]
and
[tex]x^\frac{m}{n}=\sqrt[n]{x^m}[/tex]
and
[tex](x^m)(x^n)=x^{m+n}[/tex]
so
write everybody as base 3
[tex]9=3^2[/tex]
[tex]81=9^2=(3^2)^2=3^4[/tex]
[tex](9^\frac{1}{3})(81^\frac{1}{3})=[/tex]
[tex]((3^2)^\frac{1}{3})((3^4)^\frac{1}{3})=[/tex]
[tex](3^\frac{2}{3})(3^\frac{4}{3})=[/tex]
[tex]3^\frac{2+4}{3}=[/tex]
[tex]3^{6}{3}=[/tex]
[tex]3^2=[/tex]
[tex]9[/tex]
