[tex]3^2 \cdot \cfrac{1 - 3^{-4}}{1-3^{-2}} [/tex]
[tex]= 3^2 \times (1 - 3^{-4}) \div (1 - 3^{-2}) [/tex]
[tex]= 3^2 \times (1 - \cfrac{1}{3^4} ) \div (1 - \cfrac{1}{3^2} ) [/tex]
[tex]= 9 \times (1 - \cfrac{1}{81} ) \div (1 - \cfrac{1}{9} ) [/tex]
[tex]= 9 \times \cfrac{80}{81} \div \cfrac{8}{9}[/tex]
[tex]= 9 \times \cfrac{80}{81} \times \cfrac{9}{8}[/tex]
[tex]= 10[/tex]
