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The expression provided is:

\[
\sqrt[3]{\frac{64}{125}}
\]

To simplify this, we can break it into two parts: simplify the cube roots of both the numerator (64) and the denominator (125).

1. The cube root of 64 is:
\[
\sqrt[3]{64} = \sqrt[3]{4^3} = 4
\]

2. The cube root of 125 is:
\[
\sqrt[3]{125} = \sqrt[3]{5^3} = 5
\]

So, the simplified form of the expression is:
\[
\frac{4}{5}
\]

The answer is \(\frac{4}{5}\).

Would you like further details or have any other questions? Here are 5 related questions to expand on this topic:

1. How do you simplify expressions with higher roots, like 4th or 5th roots?
2. What are the properties of cube roots, and how do they differ from square roots?
3. How would you handle cube roots of negative numbers?
4. Can you generalize how to simplify roots of fractions?
5. How would this expression change if the powers were different, say a square root instead of a cube root?

**Tip**: When simplifying roots of fractions, always try to factor the numerator and denominator separately to check if perfect powers exist.

Simplify the cube root of 64 divided by 125.

Learn how to simplify the cube root of the fraction 64 divided by 125. This problem teaches essential concepts of cube roots and fractions, breaking the solution into step-by-step parts. Suitable for Grades 8-10.

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