Answer
$\frac{1}{9}$
Work Step by Step
We are given the expression $(3^{-1})^{2}$.
To simplify, we can use the power rule, which holds that $(a^{m})^{n}=a^{m\times n}$ (where a is a real number, and m and n are integers).
$(3^{-1})^{2}=3^{-1\times2}=3^{-2}$
To simplify this into a positive exponent, we know that $a^{-n}=\frac{1}{a^{n}}$ (where a is a nonzero real number and n is a positive integer).
Therefore, $3^{-2}=\frac{1}{3^{2}}=\frac{1}{3\times3}=\frac{1}{9}$
