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.