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Answer :
To evaluate the expression [tex]\(\frac{1}{5^{-2}}\)[/tex], we can use the property of exponents that states [tex]\(a^{-n} = \frac{1}{a^n}\)[/tex]. Here's a step-by-step explanation:
1. Understand the expression: Start with the expression [tex]\(\frac{1}{5^{-2}}\)[/tex].
2. Use the rule of negative exponents: The negative exponent means we take the reciprocal of the base raised to the positive of that exponent. Specifically, [tex]\(5^{-2}\)[/tex] can be rewritten as [tex]\(\frac{1}{5^2}\)[/tex].
3. Simplify the expression: Substitute [tex]\(\frac{1}{5^2}\)[/tex] in the place of [tex]\(5^{-2}\)[/tex], resulting in:
[tex]\[
\frac{1}{\frac{1}{5^2}} = 5^2
\][/tex]
4. Calculate [tex]\(5^2\)[/tex]: This means 5 raised to the power of 2, which is:
[tex]\[
5 \times 5 = 25
\][/tex]
So, the expression [tex]\(\frac{1}{5^{-2}}\)[/tex] simplifies to 25.
Therefore, the correct answer is [tex]\(25\)[/tex].
1. Understand the expression: Start with the expression [tex]\(\frac{1}{5^{-2}}\)[/tex].
2. Use the rule of negative exponents: The negative exponent means we take the reciprocal of the base raised to the positive of that exponent. Specifically, [tex]\(5^{-2}\)[/tex] can be rewritten as [tex]\(\frac{1}{5^2}\)[/tex].
3. Simplify the expression: Substitute [tex]\(\frac{1}{5^2}\)[/tex] in the place of [tex]\(5^{-2}\)[/tex], resulting in:
[tex]\[
\frac{1}{\frac{1}{5^2}} = 5^2
\][/tex]
4. Calculate [tex]\(5^2\)[/tex]: This means 5 raised to the power of 2, which is:
[tex]\[
5 \times 5 = 25
\][/tex]
So, the expression [tex]\(\frac{1}{5^{-2}}\)[/tex] simplifies to 25.
Therefore, the correct answer is [tex]\(25\)[/tex].
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