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Answer :
To find the equivalent expression for [tex]\(5^{-2}\)[/tex], we use the rule of negative exponents. The rule tells us that a negative exponent means we take the reciprocal of the base raised to the positive of that exponent. In mathematical terms:
[tex]\[ a^{-b} = \frac{1}{a^b} \][/tex]
For the expression [tex]\(5^{-2}\)[/tex]:
1. Identify the base and the negative exponent. Here, the base is 5 and the exponent is -2.
2. Apply the rule: [tex]\(5^{-2} = \frac{1}{5^2}\)[/tex].
Now, compute [tex]\(5^2\)[/tex]:
- [tex]\(5^2 = 5 \times 5 = 25\)[/tex].
Using this result, substitute back into the fraction:
[tex]\[ 5^{-2} = \frac{1}{25} \][/tex]
So, the expression [tex]\(5^{-2}\)[/tex] is equivalent to [tex]\(\frac{1}{25}\)[/tex].
Looking at the choices:
- A. [tex]\(\frac{1}{10}\)[/tex]
- B. [tex]\(-\frac{1}{25}\)[/tex]
- C. [tex]\(-10\)[/tex]
- D. [tex]\(\frac{1}{25}\)[/tex]
The correct choice is D. [tex]\(\frac{1}{25}\)[/tex].
[tex]\[ a^{-b} = \frac{1}{a^b} \][/tex]
For the expression [tex]\(5^{-2}\)[/tex]:
1. Identify the base and the negative exponent. Here, the base is 5 and the exponent is -2.
2. Apply the rule: [tex]\(5^{-2} = \frac{1}{5^2}\)[/tex].
Now, compute [tex]\(5^2\)[/tex]:
- [tex]\(5^2 = 5 \times 5 = 25\)[/tex].
Using this result, substitute back into the fraction:
[tex]\[ 5^{-2} = \frac{1}{25} \][/tex]
So, the expression [tex]\(5^{-2}\)[/tex] is equivalent to [tex]\(\frac{1}{25}\)[/tex].
Looking at the choices:
- A. [tex]\(\frac{1}{10}\)[/tex]
- B. [tex]\(-\frac{1}{25}\)[/tex]
- C. [tex]\(-10\)[/tex]
- D. [tex]\(\frac{1}{25}\)[/tex]
The correct choice is D. [tex]\(\frac{1}{25}\)[/tex].
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