https://file.aiquickdraw.com/mathbot/file/1727186458870btz1n6x6.jpg

The expression in the image is:

\[
(625)^{-\frac{1}{4}}
\]

To solve this, follow these steps:

1. First, recognize that \(625^{-\frac{1}{4}}\) means taking the fourth root of 625 and then applying the negative exponent, which will take the reciprocal of the result.
   
2. The fourth root of 625 is 5, because:
   \[
   5^4 = 625
   \]

3. Applying the negative exponent gives:
   \[
   (625)^{-\frac{1}{4}} = \frac{1}{5}
   \]

Thus, the result is \( \frac{1}{5} \) or 0.2.

Do you want more details or have any questions?

Here are some related questions for deeper understanding:
1. What is the cube root of \( (343)^{-\frac{1}{3}} \)?
2. How would you solve \( 81^{-\frac{1}{2}} \)?
3. What is the general rule for solving \( x^{-\frac{m}{n}} \)?
4. How does the reciprocal property of negative exponents work?
5. What is the value of \( (16)^{\frac{1}{4}} \)?

**Tip:** Always simplify the root first before applying any negative exponent in expressions like these!

Learn how to solve (625)^(-1/4) by applying the properties of exponents. This problem involves finding the fourth root of 625 and using the reciprocal property of negative exponents. Suitable for students in Grades 9-11.

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