Let's analyze the given mathematical expression step-by-step to determine its value and the corresponding true statement about it.
Consider the expression:
[tex]\[
\left(5^{-1}\right)^2
\][/tex]
### Step 1: Calculate [tex]\(5^{-1}\)[/tex]
An exponent of -1 indicates the reciprocal of the number. Thus, [tex]\(5^{-1}\)[/tex] can be calculated as:
[tex]\[
5^{-1} = \frac{1}{5}
\][/tex]
[tex]\[
5^{-1} = 0.2
\][/tex]
### Step 2: Square the Result
We now need to square the result obtained in Step 1:
[tex]\[
(0.2)^2 = 0.2 \times 0.2
\][/tex]
[tex]\[
(0.2)^2 = 0.04
\][/tex]
So, the value of the expression [tex]\(\left(5^{-1}\right)^2\)[/tex] is [tex]\(0.04\)[/tex].
### Step 3: Determine the Appropriate Statement
Now we need to evaluate the given statements in the question:
1. It is less than -1: [tex]\(0.04\)[/tex] is not less than -1.
2. It is between 0 and 1: [tex]\(0.04\)[/tex] lies in the interval between 0 and 1.
3. It is between -1 and 0: [tex]\(0.04\)[/tex] is not in the interval between -1 and 0.
4. It is greater than 1: [tex]\(0.04\)[/tex] is not greater than 1.
The correct statement about the value of [tex]\(\left(5^{-1}\right)^2\)[/tex] is:
[tex]\[
\text{It is between 0 and 1.}
\][/tex]
Therefore, the true statement is:
\[
\text{It is between 0 and 1.}
\
