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Answer :
To evaluate the expression [tex]\(\frac{1}{5^{-2}}\)[/tex], let's go through the steps:
1. Understanding Negative Exponents:
A negative exponent means you take the reciprocal of the base raised to the positive of that exponent. So, [tex]\(5^{-2}\)[/tex] is the same as [tex]\(\frac{1}{5^2}\)[/tex].
2. Rewriting the Expression:
[tex]\[
\frac{1}{5^{-2}} = \frac{1}{\frac{1}{5^2}}
\][/tex]
3. Simplifying the Expression:
To simplify [tex]\(\frac{1}{\frac{1}{5^2}}\)[/tex], you multiply by the reciprocal:
[tex]\[
\frac{1}{\frac{1}{5^2}} = 5^2
\][/tex]
4. Calculating [tex]\(5^2\)[/tex]:
Calculate [tex]\(5^2\)[/tex] which is [tex]\(5 \times 5 = 25\)[/tex].
So, the value of the expression [tex]\(\frac{1}{5^{-2}}\)[/tex] is [tex]\(25\)[/tex].
1. Understanding Negative Exponents:
A negative exponent means you take the reciprocal of the base raised to the positive of that exponent. So, [tex]\(5^{-2}\)[/tex] is the same as [tex]\(\frac{1}{5^2}\)[/tex].
2. Rewriting the Expression:
[tex]\[
\frac{1}{5^{-2}} = \frac{1}{\frac{1}{5^2}}
\][/tex]
3. Simplifying the Expression:
To simplify [tex]\(\frac{1}{\frac{1}{5^2}}\)[/tex], you multiply by the reciprocal:
[tex]\[
\frac{1}{\frac{1}{5^2}} = 5^2
\][/tex]
4. Calculating [tex]\(5^2\)[/tex]:
Calculate [tex]\(5^2\)[/tex] which is [tex]\(5 \times 5 = 25\)[/tex].
So, the value of the expression [tex]\(\frac{1}{5^{-2}}\)[/tex] is [tex]\(25\)[/tex].
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