To solve the problem, we are analyzing the expression:

$\left( 5^{-1} \right)^2$

Step-by-step Solution:

1. Simplify $5^{-1}$: The negative exponent rule tells us: $5^{-1} = \frac{1}{5}.$ So, $5^{-1}$ equals $0.2$ (since $1 \div 5 = 0.2$).

2. Square $\frac{1}{5}$: Now we square $\frac{1}{5}$: $\left( \frac{1}{5} \right)^2 = \frac{1}{25}.$ In decimal form: $\frac{1}{25} = 0.04.$

3. Analyze the value $0.04$:

   • $0.04$ is positive.
   • $0.04$ is greater than 0 but less than 1.

Correct Answer:

The statement that is true about the value of the expression is:

"It is between 0 and 1."

Do you want further clarification or additional examples? Let me know!

Here are 5 related questions to expand on this concept:

1. What happens to a negative exponent when it is squared?
2. What is the value of $(3^{-1})^2$?
3. How does the negative exponent rule work for fractions?
4. What is the result of $(2^{-2})^2$?
5. How do we determine if a value is between -1 and 0?

Tip: A negative exponent means you are taking the reciprocal of the base, and squaring a small fraction always results in an even smaller positive value.