Simplify the expression:

[tex]\[ -(10)^{-2} \][/tex]

A. [tex]\(\frac{1}{10^2}\)[/tex]

B. [tex]\(-\frac{1}{-2^{10}}\)[/tex]

C. [tex]\(-\frac{1}{10^2}\)[/tex]

D. [tex]\(10^2\)[/tex]



Answer :

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]