To simplify the expression [tex]\(11^{-2}\)[/tex]:
1. Understand Negative Exponents: When dealing with a negative exponent, [tex]\(a^{-b}\)[/tex] is equivalent to [tex]\(\frac{1}{a^b}\)[/tex].
2. Apply the Rule: For [tex]\(11^{-2}\)[/tex], this translates to [tex]\(\frac{1}{11^2}\)[/tex].
3. Calculate the Denominator: Next, calculate [tex]\(11^2\)[/tex]:
[tex]\[
11^2 = 11 \times 11 = 121
\][/tex]
4. Simplify the Expression: Now, place the result in the denominator:
[tex]\[
11^{-2} = \frac{1}{121}
\][/tex]
5. Convert the Fraction to Decimal: [tex]\(\frac{1}{121}\)[/tex] is approximately [tex]\(0.008264462809917356\)[/tex].
Thus, the simplest form of the expression [tex]\(11^{-2}\)[/tex] is approximately [tex]\(0.008264462809917356\)[/tex].
