Let's simplify and evaluate each expression step-by-step:
1. Simplify the expression [tex]\(-(10)^{-2}\)[/tex]:
[tex]\[
-(10)^{-2} = -\left(\frac{1}{10^2}\right) = -\left(\frac{1}{100}\right) = -0.01
\][/tex]
2. Evaluate [tex]\(\frac{1}{10^2}\)[/tex]:
[tex]\[
\frac{1}{10^2} = \frac{1}{100} = 0.01
\][/tex]
3. Evaluate [tex]\(-\frac{1}{-2^{10}}\)[/tex]:
[tex]\[
-\frac{1}{-2^{10}} = -\frac{1}{-(1024)} = -\left(-\frac{1}{1024}\right) = \frac{1}{1024} \approx -0.0009765625
\][/tex]
4. Evaluate [tex]\(-\frac{1}{10^2}\)[/tex]:
[tex]\[
-\frac{1}{10^2} = -\frac{1}{100} = -0.01
\][/tex]
5. Evaluate [tex]\(10^2\)[/tex]:
[tex]\[
10^2 = 100
\][/tex]
So, the results of simplifying and evaluating the expressions are:
1. [tex]\( -(10)^{-2} = -0.01 \)[/tex]
2. [tex]\( \frac{1}{10^2} = 0.01 \)[/tex]
3. [tex]\( -\frac{1}{-2^{10}} \approx -0.0009765625 \)[/tex]
4. [tex]\( -\frac{1}{10^2} = -0.01 \)[/tex]
5. [tex]\( 10^2 = 100 \)[/tex]
These are the simplified results.
