https://file.aiquickdraw.com/mathbot/file/17295950589303lis78rx.jpg

The expression shown in the image is:

\[
\left( \frac{125}{512} \right)^{\frac{1}{3}}
\]

This is a cube root of the fraction \(\frac{125}{512}\). To simplify, we'll take the cube root of both the numerator and the denominator separately.

1. Cube root of \(125\):  
   \(125 = 5^3\), so \(\sqrt[3]{125} = 5\).

2. Cube root of \(512\):  
   \(512 = 8^3\), so \(\sqrt[3]{512} = 8\).

Thus, the cube root of \(\frac{125}{512}\) is:

\[
\frac{5}{8}
\]

The simplified answer is \(\frac{5}{8}\).

Would you like more details on this or have any further questions?

Here are 5 related questions to explore:
1. How do you find the cube root of a number?
2. What happens if a fraction doesn't simplify nicely under a cube root?
3. How does the cube root compare to other roots (like square roots)?
4. Can you apply cube roots to negative numbers?
5. How would you solve an expression involving higher roots, such as \(\sqrt[4]{x}\)?

**Tip:** When dealing with roots, if both the numerator and denominator are perfect powers (like squares or cubes), you can simplify them separately.

This guide walks through simplifying the cube root of the fraction 125/512. Learn how to break down the numerator and denominator into their cube roots, applying key exponent and fraction concepts. Suitable for students in Grades 8-10.

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