https://file.aiquickdraw.com/mathbot/file/1726616343998vddmfgt8.jpg

The problem you uploaded is focused on evaluating the expression \( 5^{-4} \). The structure in the image indicates steps to express it as a fraction.

Here’s how to solve it:

### Step-by-Step Solution:

1. **Base and Negative Exponent**: The expression \( 5^{-4} \) means the reciprocal of \( 5^4 \).

2. **Reciprocal Representation**: 
   \[
   5^{-4} = \frac{1}{5^4}
   \]

3. **Evaluate \( 5^4 \)**:
   \[
   5^4 = 5 \times 5 \times 5 \times 5 = 625
   \]

4. **Final Answer**:
   \[
   5^{-4} = \frac{1}{625}
   \]

So, the boxes in your image correspond to filling in \( 5^4 \) and then simplifying it to \( 625 \), making the expression:
\[
\frac{1}{625}
\]

Let me know if you have questions or would like further explanation!

### Here are 5 related questions:
1. What does \( a^{-n} \) mean in general for any base \( a \) and positive integer \( n \)?
2. How do we evaluate powers like \( 2^{-3} \)?
3. What is the value of \( 10^{-5} \) in fractional form?
4. Can negative exponents apply to fractions, such as \( \left( \frac{3}{2} \right)^{-2} \)?
5. How do we simplify expressions with both positive and negative exponents like \( 2^3 \times 2^{-2} \)?

### Tip:
When dealing with negative exponents, remember that they indicate the reciprocal of the base raised to the positive version of the exponent.

Learn how to evaluate 5^{-4} step-by-step. This problem explains the concept of negative exponents and how to convert them into fractions using reciprocal properties. Suitable for middle school students (Grades 6-8).

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