https://file.aiquickdraw.com/mathbot/file/1725408299738mbjeajvb.jpg

The image appears to be an exercise involving finding cube roots of expressions, specifically dealing with fractional bases. Let's break down the steps shown in the image.

### Steps Shown in the Image:

1. **Find the cube root of \(\frac{8}{27}\) and \(-\frac{8}{27}\):**
   - The cube root of \(\frac{8}{27}\) is expressed as \(\sqrt[3]{\frac{8}{27}}\).
   - Similarly, the cube root of \(-\frac{8}{27}\) is expressed as \(\sqrt[3]{-\frac{8}{27}}\).

2. **Calculating Cube Roots:**
   - For \(\sqrt[3]{\frac{8}{27}}\):
     - Recognize that \(\frac{8}{27} = \frac{2^3}{3^3}\).
     - Therefore, \(\sqrt[3]{\frac{8}{27}} = \frac{\sqrt[3]{8}}{\sqrt[3]{27}} = \frac{2}{3}\).
   - For \(\sqrt[3]{-\frac{8}{27}}\):
     - Similarly, \(\sqrt[3]{-\frac{8}{27}} = -\frac{\sqrt[3]{8}}{\sqrt[3]{27}} = -\frac{2}{3}\).

3. **Conclusion:**
   - The cube root of \(\frac{8}{27}\) is \(\frac{2}{3}\).
   - The cube root of \(-\frac{8}{27}\) is \(-\frac{2}{3}\).

### Summary:

- The cube roots of \(\frac{8}{27}\) and \(-\frac{8}{27}\) are \(\frac{2}{3}\) and \(-\frac{2}{3}\), respectively.
  
### Would you like more details or have any questions about the steps involved?

Here are five questions to further explore the topic:

1. What is the general rule for finding the cube root of a fraction?
2. How do you simplify cube roots involving negative numbers?
3. How does the concept of cube roots apply to real-world situations?
4. What happens when you cube the result of the cube root of a fraction?
5. Can you find the cube root of a complex number using similar steps?

**Tip:** Always remember that the cube root of a negative number will be negative, while the cube root of a positive number will be positive.

Find the cube root of \(\frac{8}{27}\) and \(-\frac{8}{27}\).

Learn how to find the cube roots of fractions \(\frac{8}{27}\) and \(-\frac{8}{27}\) with a step-by-step solution. Understand the properties of cube roots and how to simplify them, suitable for students in Grades 7-9.

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