Answer:
[tex]\frac{1}{81}[/tex]
Step-by-step explanation:
Using the rule of exponents
[tex]a^{-m}[/tex] ⇔ [tex]\frac{1}{a^{m} }[/tex]
Evaluating from the inside parenthesis outwards
[tex](-\frac{1}{3}) ^{2}[/tex] = - [tex]\frac{1}{3}[/tex] × - [tex]\frac{1}{3}[/tex] = [tex]\frac{1}{9}[/tex] , then
[tex](\frac{1}{9}) ^{-2}[/tex] = [tex]\frac{1}{9^{-2} }[/tex] = 9² = 81 , then
[tex](81)^{-1}[/tex] = [tex]\frac{1}{81}[/tex]
