https://file.aiquickdraw.com/mathbot/file/1726624267364ob1o9k6n.jpg

The expression provided in the image is:

\[
\sqrt[3]{-54} \cdot \sqrt[3]{\frac{1}{2}}
\]

Let's break it down step by step:

1. **Cube root of -54**: 
   \[
   \sqrt[3]{-54} = -\sqrt[3]{54}
   \]
   The cube root of 54 is approximately \( \sqrt[3]{54} \approx 3.78 \), so:
   \[
   \sqrt[3]{-54} \approx -3.78
   \]

2. **Cube root of \(\frac{1}{2}\)**: 
   \[
   \sqrt[3]{\frac{1}{2}} = \frac{\sqrt[3]{1}}{\sqrt[3]{2}} = \frac{1}{\sqrt[3]{2}} \approx \frac{1}{1.26} \approx 0.7937
   \]

3. **Multiplying both values**:
   \[
   -3.78 \times 0.7937 \approx -2.999 \approx -3
   \]

Thus, the value of the expression is approximately:

\[
\boxed{-3}
\]

Would you like more details or have any questions?

Here are 5 follow-up questions based on this problem:

1. How do you compute the cube root of a negative number?
2. What is the cube root of a fraction and how is it calculated?
3. Can the cube root of a number ever result in an imaginary number?
4. Why does multiplying a negative number by a positive number result in a negative number?
5. How is the cube root different from the square root in terms of properties?

**Tip**: When dealing with cube roots, remember that cube roots of negative numbers are also negative, unlike square roots, which are imaginary when the number is negative.

Evaluate: cube root of (-54) multiplied by cube root of (1/2)

This problem involves evaluating cube roots of a negative number and a fraction, and multiplying the results. Learn step-by-step how to compute the cube roots and simplify the expression, suitable for Grades 8-10.

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