To determine which expression is equivalent to [tex]\( 9^{-2} \)[/tex], we need to understand how negative exponents work.
1. Recall that a negative exponent indicates a reciprocal. Specifically, [tex]\( a^{-n} = \frac{1}{a^n} \)[/tex].
2. Apply this rule to the expression [tex]\( 9^{-2} \)[/tex]:
[tex]\[
9^{-2} = \frac{1}{9^2}
\][/tex]
3. Calculate [tex]\( 9^2 \)[/tex]:
[tex]\[
9^2 = 9 \times 9 = 81
\][/tex]
4. Substitute this back into the reciprocal:
[tex]\[
9^{-2} = \frac{1}{81}
\][/tex]
Therefore, the equivalent expression to [tex]\( 9^{-2} \)[/tex] is:
[tex]\[
\boxed{\frac{1}{81}}
\][/tex]
