Answer :
Let's simplify each of the given expressions one by one.
1. Simplify \(-(10)^{-2}\):
- First, evaluate \(10^{-2}\). This means taking the reciprocal of \(10^2\).
[tex]\[ 10^{-2} = \frac{1}{10^2} = \frac{1}{100} \][/tex]
- Then, apply the negative sign outside the expression:
[tex]\[ -(10^{-2}) = -\left(\frac{1}{100}\right) = -0.01 \][/tex]
2. Simplify \(-\frac{1}{-2^{10}}\):
- Begin by calculating the exponent part, \(2^{10}\):
[tex]\[ 2^{10} = 1024 \][/tex]
- Then, substitute this back into the expression:
[tex]\[ -\frac{1}{-2^{10}} = -\frac{1}{-1024} \][/tex]
- Simplifying the negative signs (a negative divided by a negative is positive):
[tex]\[ -\frac{1}{-1024} = \frac{1}{1024} = 0.0009765625 \][/tex]
3. Simplify \(\frac{1}{10^2}\):
- Calculate \(10^2\):
[tex]\[ 10^2 = 100 \][/tex]
- Then, take the reciprocal:
[tex]\[ \frac{1}{10^2} = \frac{1}{100} = 0.01 \][/tex]
4. Simplify \(-\frac{1}{10^2}\):
- Calculate \(10^2\):
[tex]\[ 10^2 = 100 \][/tex]
- Then, take the reciprocal and apply the negative sign:
[tex]\[ -\frac{1}{10^2} = -\frac{1}{100} = -0.01 \][/tex]
5. Simplify \(10^2\):
- Simply calculate the value of the exponent:
[tex]\[ 10^2 = 100 \][/tex]
The simplified expressions are:
[tex]\[ -(10)^{-2} = -0.01 \][/tex]
[tex]\[ -\frac{1}{-2^{10}} = 0.0009765625 \][/tex]
[tex]\[ \frac{1}{10^2} = 0.01 \][/tex]
[tex]\[ -\frac{1}{10^2} = -0.01 \][/tex]
[tex]\[ 10^2 = 100 \][/tex]
These are the simplified results for each expression.
1. Simplify \(-(10)^{-2}\):
- First, evaluate \(10^{-2}\). This means taking the reciprocal of \(10^2\).
[tex]\[ 10^{-2} = \frac{1}{10^2} = \frac{1}{100} \][/tex]
- Then, apply the negative sign outside the expression:
[tex]\[ -(10^{-2}) = -\left(\frac{1}{100}\right) = -0.01 \][/tex]
2. Simplify \(-\frac{1}{-2^{10}}\):
- Begin by calculating the exponent part, \(2^{10}\):
[tex]\[ 2^{10} = 1024 \][/tex]
- Then, substitute this back into the expression:
[tex]\[ -\frac{1}{-2^{10}} = -\frac{1}{-1024} \][/tex]
- Simplifying the negative signs (a negative divided by a negative is positive):
[tex]\[ -\frac{1}{-1024} = \frac{1}{1024} = 0.0009765625 \][/tex]
3. Simplify \(\frac{1}{10^2}\):
- Calculate \(10^2\):
[tex]\[ 10^2 = 100 \][/tex]
- Then, take the reciprocal:
[tex]\[ \frac{1}{10^2} = \frac{1}{100} = 0.01 \][/tex]
4. Simplify \(-\frac{1}{10^2}\):
- Calculate \(10^2\):
[tex]\[ 10^2 = 100 \][/tex]
- Then, take the reciprocal and apply the negative sign:
[tex]\[ -\frac{1}{10^2} = -\frac{1}{100} = -0.01 \][/tex]
5. Simplify \(10^2\):
- Simply calculate the value of the exponent:
[tex]\[ 10^2 = 100 \][/tex]
The simplified expressions are:
[tex]\[ -(10)^{-2} = -0.01 \][/tex]
[tex]\[ -\frac{1}{-2^{10}} = 0.0009765625 \][/tex]
[tex]\[ \frac{1}{10^2} = 0.01 \][/tex]
[tex]\[ -\frac{1}{10^2} = -0.01 \][/tex]
[tex]\[ 10^2 = 100 \][/tex]
These are the simplified results for each expression.
