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Answer :
To evaluate the expression
$$
\frac{1}{5^{-2}},
$$
follow these steps:
1. Recognize that a negative exponent means taking the reciprocal of the base raised to the positive exponent. Thus,
$$
5^{-2} = \frac{1}{5^2} = \frac{1}{25}.
$$
2. Substitute this result back into the original expression:
$$
\frac{1}{5^{-2}} = \frac{1}{\frac{1}{25}}.
$$
3. Dividing by a fraction is equivalent to multiplying by its reciprocal. Therefore,
$$
\frac{1}{\frac{1}{25}} = 1 \times 25 = 25.
$$
Thus, the value of the expression is $\boxed{25}$.
$$
\frac{1}{5^{-2}},
$$
follow these steps:
1. Recognize that a negative exponent means taking the reciprocal of the base raised to the positive exponent. Thus,
$$
5^{-2} = \frac{1}{5^2} = \frac{1}{25}.
$$
2. Substitute this result back into the original expression:
$$
\frac{1}{5^{-2}} = \frac{1}{\frac{1}{25}}.
$$
3. Dividing by a fraction is equivalent to multiplying by its reciprocal. Therefore,
$$
\frac{1}{\frac{1}{25}} = 1 \times 25 = 25.
$$
Thus, the value of the expression is $\boxed{25}$.
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