How many different values are represented by the following quantities? $$3^{-2}, 9^{-2}, 27^{-\frac{2}{3}}, 9\cdot81^{-1}, 243^{-\frac{4}{5}}$$
+128473 \( 3^{-2}, 9^{-2}, 27^{-\frac{2}{3}} \)
3^(-2) = 1 /3^2 =1 / 9
9^(-2) = 1/9^2 = 1 / 81
27^(-2/3) = 1 / [ 27]^(2/3) = 1 / [ 27^(1/3) ] ^2 = 1/ (3)^2 = 1/ 9
\(9\cdot81^{-1}, 243^{-\frac{4}{5}}\)
9 * 81^(-1) = 9 /81 = 1/9
243^(-4/5) = 1 / [ 243^(4/5) ] = 1 / [243^(1/5) ]^4 = 1/ [ 3]^4 = 1 / 81
