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Answer :
To solve the problem of finding which option is the same as [tex]\(5^{-2}\)[/tex], we can understand and calculate this expression step by step:
1. Understanding Negative Exponents:
A negative exponent means the reciprocal of the base raised to the positive of that exponent. So, [tex]\(5^{-2}\)[/tex] means we take the reciprocal of [tex]\(5^2\)[/tex].
2. Calculating [tex]\(5^2\)[/tex]:
First, let's calculate [tex]\(5^2\)[/tex]. This means multiplying 5 by itself:
[tex]\[
5^2 = 5 \times 5 = 25
\][/tex]
3. Taking the Reciprocal:
Since [tex]\(5^{-2}\)[/tex] is the reciprocal of [tex]\(5^2\)[/tex], we take the reciprocal of 25:
[tex]\[
5^{-2} = \frac{1}{25}
\][/tex]
4. Final Check:
The value [tex]\(\frac{1}{25}\)[/tex] is equivalent to the decimal 0.04, as seen from calculations.
The correct answer, therefore, is [tex]\(\frac{1}{25}\)[/tex].
1. Understanding Negative Exponents:
A negative exponent means the reciprocal of the base raised to the positive of that exponent. So, [tex]\(5^{-2}\)[/tex] means we take the reciprocal of [tex]\(5^2\)[/tex].
2. Calculating [tex]\(5^2\)[/tex]:
First, let's calculate [tex]\(5^2\)[/tex]. This means multiplying 5 by itself:
[tex]\[
5^2 = 5 \times 5 = 25
\][/tex]
3. Taking the Reciprocal:
Since [tex]\(5^{-2}\)[/tex] is the reciprocal of [tex]\(5^2\)[/tex], we take the reciprocal of 25:
[tex]\[
5^{-2} = \frac{1}{25}
\][/tex]
4. Final Check:
The value [tex]\(\frac{1}{25}\)[/tex] is equivalent to the decimal 0.04, as seen from calculations.
The correct answer, therefore, is [tex]\(\frac{1}{25}\)[/tex].
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