https://r2.erweima.ai/mathbot/image/17239463532842qhnpajk.jpg

The expression to simplify is:

\[
2 \sqrt[3]{-16} - \sqrt[3]{-54}
\]

Let's break down the terms:

1. \( \sqrt[3]{-16} = -\sqrt[3]{16} \). Since \( 16 = 2^4 \), we have:

\[
\sqrt[3]{16} = \sqrt[3]{2^4} = 2^{\frac{4}{3}} = \sqrt[3]{2^3 \times 2} = 2\sqrt[3]{2}
\]

Thus:

\[
\sqrt[3]{-16} = -2\sqrt[3]{2}
\]

So the first term is:

\[
2 \times (-2\sqrt[3]{2}) = -4\sqrt[3]{2}
\]

2. \( \sqrt[3]{-54} = -\sqrt[3]{54} \). Since \( 54 = 2 \times 3^3 \), we have:

\[
\sqrt[3]{54} = 3\sqrt[3]{2}
\]

So:

\[
\sqrt[3]{-54} = -3\sqrt[3]{2}
\]

Now, the expression becomes:

\[
-4\sqrt[3]{2} - (-3\sqrt[3]{2})
\]

This simplifies to:

\[
-4\sqrt[3]{2} + 3\sqrt[3]{2} = -\sqrt[3]{2}
\]

The simplified expression is:

\[
-\sqrt[3]{2}
\]

Would you like more details or have any questions?

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Here are 5 related questions:

1. How do you simplify expressions involving cube roots and other radicals?
2. Can cube roots be simplified similarly to square roots?
3. What are the properties of cube roots of negative numbers?
4. How can you express cube roots in terms of fractional exponents?
5. Why does the cube root of a negative number remain negative?

**Tip:** Remember, unlike square roots, cube roots of negative numbers are well-defined and remain negative.

Learn how to simplify cube root expressions: -4∛(-16) - ∛(-54). This problem involves cube roots of negative numbers and their simplification. Get a step-by-step solution and understand the properties of cube roots. Suitable for high school students.

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