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## Sagot :

1.

**Understanding Negative Exponents:**

By the rules of exponents, a negative exponent [tex]\(a^{-n}\)[/tex] can be rewritten as [tex]\(\frac{1}{a^n}\)[/tex].

Therefore, [tex]\(\left(\frac{1}{5}\right)^{-2}\)[/tex] can be transformed using this rule.

2.

**Rewriting the Expression:**

Applying the rule:

[tex]\[ \left(\frac{1}{5}\right)^{-2} = \frac{1}{\left(\frac{1}{5}\right)^2} = \frac{1}{\frac{1}{25}} \][/tex]

3.

**Simplifying the Fraction:**

[tex]\(\frac{1}{\frac{1}{25}}\)[/tex] is the reciprocal of [tex]\(\frac{1}{25}\)[/tex].

The reciprocal of [tex]\(\frac{1}{25}\)[/tex] is 25.

Therefore:

[tex]\[ \frac{1}{\frac{1}{25}} = 25 \][/tex]

Thus, the value of the expression [tex]\(\left(\frac{1}{5}\right)^{-2}\)[/tex] is [tex]\(25\)[/tex].

So, the correct number to fill in the squares is:

[tex]\[ \boxed{25} \][/tex]

The possible answers given [tex]\(2^{\frac{1}{8}}, \frac{5}{2}, \frac{1}{9}\)[/tex] are incorrect as they do not match the correct simplified result [tex]\(25\)[/tex]. The correct answer from the provided choices would be not listed, so you should manually input [tex]\(25\)[/tex] as the result.