https://file.aiquickdraw.com/mathbot/file/1726030816262aj6puj50.jpg

The expression in the image is:

\[
\frac{\sqrt[3]{3}}{\sqrt[3]{192}}
\]

To simplify this, we can rewrite it as a single cube root:

\[
\frac{\sqrt[3]{3}}{\sqrt[3]{192}} = \sqrt[3]{\frac{3}{192}}
\]

Now, simplify \(\frac{3}{192}\):

\[
\frac{3}{192} = \frac{1}{64}
\]

Thus, the expression becomes:

\[
\sqrt[3]{\frac{1}{64}} = \frac{1}{\sqrt[3]{64}}
\]

Since \(64 = 4^3\), we can simplify further:

\[
\frac{1}{\sqrt[3]{64}} = \frac{1}{4}
\]

Therefore, the simplified result is:

\[
\frac{1}{4}
\]

Would you like a further breakdown of the steps or have any questions?

Here are some related questions:
1. How do you simplify cube roots involving fractions?
2. What is the cube root of a number and how do we calculate it manually?
3. Can cube roots be simplified similarly to square roots?
4. What are the properties of cube roots of negative numbers?
5. How would this change if you had a square root instead of a cube root?

**Tip:** When simplifying cube roots involving fractions, combine the terms under one root to see if the fraction can be simplified before evaluating the root.

Simplify the expression involving cube roots: cube root of 3 over cube root of 192.

Learn how to simplify the expression involving cube roots, starting from the cube root of 3 over the cube root of 192 and reducing it to 1/4. This tutorial covers the simplification of fractions under cube roots and the properties of radicals.

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