Certainly! Let's simplify each of the given expressions step-by-step:
### Expression 1: [tex]\(-(10)^{-2}\)[/tex]
To simplify [tex]\(-(10)^{-2}\)[/tex], follow these steps:
1. First, understand that [tex]\((10)^{-2}\)[/tex] indicates the reciprocal of [tex]\(10^2\)[/tex].
[tex]\[
(10)^{-2} = \frac{1}{10^2} = \frac{1}{100}
\][/tex]
2. Applying the negative sign:
[tex]\[
-(10)^{-2} = -\left(\frac{1}{100}\right) = -0.01
\][/tex]
Thus, the simplified form of [tex]\(-(10)^{-2}\)[/tex] is:
[tex]\[
-0.01
\][/tex]
### Expression 2: [tex]\(\frac{1}{10^2}\)[/tex]
To simplify [tex]\(\frac{1}{10^2}\)[/tex], follow these steps:
1. Calculate [tex]\(10^2\)[/tex]:
[tex]\[
10^2 = 100
\][/tex]
2. Since we have the reciprocal:
[tex]\[
\frac{1}{10^2} = \frac{1}{100} = 0.01
\][/tex]
Thus, the simplified form of [tex]\(\frac{1}{10^2}\)[/tex] is:
[tex]\[
0.01
\][/tex]
### Expression 3: [tex]\(-\frac{1}{-2^{10}}\)[/tex]
To simplify [tex]\(-\frac{1}{-2^{10}}\)[/tex], follow these steps:
1. Calculate [tex]\(-2^{10}\)[/tex]:
[tex]\[
-2^{10} = -1024
\][/tex]
2. Since we have a negative reciprocal:
[tex]\[
-\frac{1}{-1024} = \frac{1}{1024}
\][/tex]
3. [tex]\(\frac{1}{1024} = 0.0009765625\)[/tex]
Thus, the simplified form of [tex]\(-\frac{1}{-2^{10}}\)[/tex] is:
[tex]\[
0.0009765625
\][/tex]
### Expression 4: [tex]\(-\frac{1}{10^2}\)[/tex]
To simplify [tex]\(-\frac{1}{10^2}\)[/tex], follow these steps:
1. Calculate [tex]\(10^2\)[/tex]:
[tex]\[
10^2 = 100
\][/tex]
2. Apply the negative sign:
[tex]\[
-\frac{1}{10^2} = -\frac{1}{100} = -0.01
\][/tex]
Thus, the simplified form of [tex]\(-\frac{1}{10^2}\)[/tex] is:
[tex]\[
-0.01
\][/tex]
### Expression 5: [tex]\(10^2\)[/tex]
To simplify [tex]\(10^2\)[/tex], follow these steps:
1. Calculate:
[tex]\[
10^2 = 100
\][/tex]
Thus, the simplified form of [tex]\(10^2\)[/tex] is:
[tex]\[
100
\][/tex]
### Summary
The simplified forms of the given expressions are:
1. [tex]\(-(10)^{-2}\)[/tex] = [tex]\(-0.01\)[/tex]
2. [tex]\(\frac{1}{10^2}\)[/tex] = [tex]\(0.01\)[/tex]
3. [tex]\(-\frac{1}{-2^{10}}\)[/tex] = [tex]\(0.0009765625\)[/tex]
4. [tex]\(-\frac{1}{10^2}\)[/tex] = [tex]\(-0.01\)[/tex]
5. [tex]\(10^2\)[/tex] = [tex]\(100\)[/tex]
Hence, the final answer is:
[tex]\[
(-0.01, 0.01, 0.0009765625, -0.01, 100)
\][/tex]
