The expression \(\frac{6}{\sqrt[3]{-7}}\) can be simplified, though it cannot be simplified to a more elementary form without resorting to decimal approximations.

To rewrite it:

\[
\frac{6}{\sqrt[3]{-7}}
\]

This is already in its simplest form. The cube root of \(-7\) is an irrational number and doesn't simplify further.

### If you wanted to approximate the value:
\[
\sqrt[3]{-7} \approx -1.913
\]

Thus:

\[
\frac{6}{\sqrt[3]{-7}} \approx \frac{6}{-1.913} \approx -3.136
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How would you simplify the expression \(\frac{a}{\sqrt[3]{b}}\) in general?
2. What is the cube root of a negative number?
3. How do you rationalize a denominator containing a cube root?
4. How do you find the cube root of a number manually?
5. What are some common applications of cube roots in real life?

**Tip:** Remember that the cube root of a negative number is negative, unlike square roots where the principal root is usually taken as positive.

Learn how to simplify the expression \(\frac{6}{\sqrt[3]{-7}}\) with detailed explanations. Understand cube roots of negative numbers and how to handle irrational denominators. Suitable for high school students.

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