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Answer :
To evaluate the expression [tex]\(\frac{1}{5^{-2}}\)[/tex], let's go through the steps:
1. Understand the negative exponent: When you have a negative exponent, such as [tex]\(5^{-2}\)[/tex], it means you take the reciprocal of the base raised to the positive exponent. So, [tex]\(5^{-2}\)[/tex] is the same as [tex]\(\frac{1}{5^2}\)[/tex].
2. Calculate [tex]\(5^2\)[/tex]: Now, calculate [tex]\(5^2\)[/tex] which is [tex]\(5 \times 5 = 25\)[/tex].
3. Reciprocal of 25: Since [tex]\(5^{-2} = \frac{1}{25}\)[/tex], the reciprocal gives us [tex]\(5^{-2} = 0.04\)[/tex].
4. Calculate the original expression: The original expression asks for [tex]\(\frac{1}{5^{-2}}\)[/tex]. Since [tex]\(5^{-2}\)[/tex] is [tex]\(0.04\)[/tex], find [tex]\(\frac{1}{0.04}\)[/tex].
5. Final Calculation: [tex]\(\frac{1}{0.04} = 25\)[/tex].
So, [tex]\(\frac{1}{5^{-2}}\)[/tex] evaluates to 25.
1. Understand the negative exponent: When you have a negative exponent, such as [tex]\(5^{-2}\)[/tex], it means you take the reciprocal of the base raised to the positive exponent. So, [tex]\(5^{-2}\)[/tex] is the same as [tex]\(\frac{1}{5^2}\)[/tex].
2. Calculate [tex]\(5^2\)[/tex]: Now, calculate [tex]\(5^2\)[/tex] which is [tex]\(5 \times 5 = 25\)[/tex].
3. Reciprocal of 25: Since [tex]\(5^{-2} = \frac{1}{25}\)[/tex], the reciprocal gives us [tex]\(5^{-2} = 0.04\)[/tex].
4. Calculate the original expression: The original expression asks for [tex]\(\frac{1}{5^{-2}}\)[/tex]. Since [tex]\(5^{-2}\)[/tex] is [tex]\(0.04\)[/tex], find [tex]\(\frac{1}{0.04}\)[/tex].
5. Final Calculation: [tex]\(\frac{1}{0.04} = 25\)[/tex].
So, [tex]\(\frac{1}{5^{-2}}\)[/tex] evaluates to 25.
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