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Answer :
To express [tex]\(\frac{1}{25}\)[/tex] as a power of [tex]\(s\)[/tex], let's break it down step by step:
1. Understand the fraction: We start with the fraction [tex]\(\frac{1}{25}\)[/tex]. This can be thought of as a reciprocal, which can also be expressed as [tex]\(25^{-1}\)[/tex].
2. Rewrite the denominator as a power: We recognize that [tex]\(25\)[/tex] is a perfect square. Specifically, [tex]\(25 = 5^2\)[/tex].
3. Apply the exponent rules: Now, let's apply exponent rules to express [tex]\(\frac{1}{25}\)[/tex] as a power of [tex]\(s\)[/tex].
- Since [tex]\(25 = 5^2\)[/tex], we have [tex]\(\frac{1}{25} = (5^2)^{-1}\)[/tex].
- According to the rule of exponents [tex]\((a^b)^c = a^{b \times c}\)[/tex], we can simplify [tex]\((5^2)^{-1}\)[/tex] as [tex]\(5^{2 \times (-1)}\)[/tex].
4. Calculate the exponent: Perform the multiplication in the exponent:
- [tex]\(2 \times (-1) = -2\)[/tex].
5. Final expression: Therefore, [tex]\(\frac{1}{25}\)[/tex] is expressed as [tex]\(5^{-2}\)[/tex].
In conclusion, [tex]\(\frac{1}{25}\)[/tex] expressed as a power of [tex]\(s\)[/tex] is [tex]\(5^{-2}\)[/tex].
1. Understand the fraction: We start with the fraction [tex]\(\frac{1}{25}\)[/tex]. This can be thought of as a reciprocal, which can also be expressed as [tex]\(25^{-1}\)[/tex].
2. Rewrite the denominator as a power: We recognize that [tex]\(25\)[/tex] is a perfect square. Specifically, [tex]\(25 = 5^2\)[/tex].
3. Apply the exponent rules: Now, let's apply exponent rules to express [tex]\(\frac{1}{25}\)[/tex] as a power of [tex]\(s\)[/tex].
- Since [tex]\(25 = 5^2\)[/tex], we have [tex]\(\frac{1}{25} = (5^2)^{-1}\)[/tex].
- According to the rule of exponents [tex]\((a^b)^c = a^{b \times c}\)[/tex], we can simplify [tex]\((5^2)^{-1}\)[/tex] as [tex]\(5^{2 \times (-1)}\)[/tex].
4. Calculate the exponent: Perform the multiplication in the exponent:
- [tex]\(2 \times (-1) = -2\)[/tex].
5. Final expression: Therefore, [tex]\(\frac{1}{25}\)[/tex] is expressed as [tex]\(5^{-2}\)[/tex].
In conclusion, [tex]\(\frac{1}{25}\)[/tex] expressed as a power of [tex]\(s\)[/tex] is [tex]\(5^{-2}\)[/tex].
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