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Answer :
- Use the property $a^{-n} = \frac{1}{a^n}$ to rewrite $5^{-2}$ as $\frac{1}{5^2}$.
- Calculate $5^2 = 25$.
- Determine the value of $\frac{1}{5^2} = \frac{1}{25}$.
- The final answer is $\boxed{\frac{1}{25}}$.
### Explanation
1. Understanding the problem
We are asked to find the value of $5^{-2}$. We need to use the property of exponents that states $a^{-n} = \frac{1}{a^n}$.
2. Rewriting the expression
Applying the property, we can rewrite $5^{-2}$ as $\frac{1}{5^2}$.
3. Calculating the square
Now, we need to calculate $5^2$, which means $5 \times 5$. The result of this calculation is 25.
4. Finding the final value
Therefore, $5^{-2} = \frac{1}{5^2} = \frac{1}{25}$. Comparing this result with the given options, we find that option B matches our calculated value.
### Examples
Understanding exponent properties is crucial in various fields, such as calculating compound interest, where the exponent represents the number of compounding periods. For instance, if you invest money in a bank account with compound interest, the formula involves raising the interest rate plus one to the power of the number of years. This concept also applies in physics, such as calculating the decay of radioactive substances or the growth of bacterial populations.
- Calculate $5^2 = 25$.
- Determine the value of $\frac{1}{5^2} = \frac{1}{25}$.
- The final answer is $\boxed{\frac{1}{25}}$.
### Explanation
1. Understanding the problem
We are asked to find the value of $5^{-2}$. We need to use the property of exponents that states $a^{-n} = \frac{1}{a^n}$.
2. Rewriting the expression
Applying the property, we can rewrite $5^{-2}$ as $\frac{1}{5^2}$.
3. Calculating the square
Now, we need to calculate $5^2$, which means $5 \times 5$. The result of this calculation is 25.
4. Finding the final value
Therefore, $5^{-2} = \frac{1}{5^2} = \frac{1}{25}$. Comparing this result with the given options, we find that option B matches our calculated value.
### Examples
Understanding exponent properties is crucial in various fields, such as calculating compound interest, where the exponent represents the number of compounding periods. For instance, if you invest money in a bank account with compound interest, the formula involves raising the interest rate plus one to the power of the number of years. This concept also applies in physics, such as calculating the decay of radioactive substances or the growth of bacterial populations.
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