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Answer :
- Calculate $5^{-2}$ using the property $a^{-n} = \frac{1}{a^n}$, which gives $\frac{1}{5^2} = \frac{1}{25}$.
- Compare the calculated value with the given options.
- The correct option is $\frac{1}{25}$.
- Therefore, the final answer is $\boxed{\frac{1}{25}}$.
### Explanation
1. Understanding the problem
We are asked to find the value of $5^{-2}$ from the given options. The options are: -10, -1/25, 1/25, 3
2. Calculating the value
We need to calculate $5^{-2}$ using the property $a^{-n} = \frac{1}{a^n}$. So, $5^{-2} = \frac{1}{5^2} = \frac{1}{25}$.
3. Comparing with the options
Now, we compare the calculated value with the given options. The options are: -10, -$\frac{1}{25}$, $\frac{1}{25}$, 3. The correct option is $\frac{1}{25}$.
4. Final Answer
Therefore, $5^{-2} = \frac{1}{25}$.
### Examples
Understanding negative exponents is crucial in various fields, such as calculating the decay rate of radioactive materials or determining the depreciation of assets over time. For instance, if a substance decays at a rate proportional to $2^{-t}$, where $t$ is time, knowing how to evaluate negative exponents helps predict the remaining amount of the substance after a certain period.
- Compare the calculated value with the given options.
- The correct option is $\frac{1}{25}$.
- Therefore, the final answer is $\boxed{\frac{1}{25}}$.
### Explanation
1. Understanding the problem
We are asked to find the value of $5^{-2}$ from the given options. The options are: -10, -1/25, 1/25, 3
2. Calculating the value
We need to calculate $5^{-2}$ using the property $a^{-n} = \frac{1}{a^n}$. So, $5^{-2} = \frac{1}{5^2} = \frac{1}{25}$.
3. Comparing with the options
Now, we compare the calculated value with the given options. The options are: -10, -$\frac{1}{25}$, $\frac{1}{25}$, 3. The correct option is $\frac{1}{25}$.
4. Final Answer
Therefore, $5^{-2} = \frac{1}{25}$.
### Examples
Understanding negative exponents is crucial in various fields, such as calculating the decay rate of radioactive materials or determining the depreciation of assets over time. For instance, if a substance decays at a rate proportional to $2^{-t}$, where $t$ is time, knowing how to evaluate negative exponents helps predict the remaining amount of the substance after a certain period.
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