https://file.aiquickdraw.com/mathbot/file/172766355839032tkeevj.jpg

The expression to simplify is:

\[
-\sqrt[3]{16} - 4\sqrt[3]{54}
\]

Let's work through the simplification step-by-step:

### Step 1: Break down the cube roots

- \(\sqrt[3]{16}\) is not a perfect cube, but it can be approximated or simplified if needed. 
- \(\sqrt[3]{54}\) is also not a perfect cube, but it can be factored.

### Step 2: Approximate cube roots

- \(\sqrt[3]{16} \approx 2.52\)
- \(\sqrt[3]{54} \approx 3.78\)

### Step 3: Substitute the approximations

\[
-\sqrt[3]{16} - 4\sqrt[3]{54} \approx -2.52 - 4(3.78)
\]

Simplifying further:

\[
-2.52 - 15.12 = -17.64
\]

So, the simplified approximation of the expression is approximately:

\[
-17.64
\]

Let me know if you need further clarifications or more details on each step! Would you like to see the exact cube root values or any other explanation?

Here are 5 related questions for further practice:
1. How would you simplify \(\sqrt[3]{8} - 3\sqrt[3]{27}\)?
2. What are the properties of cube roots for simplifying expressions?
3. Can \(\sqrt[3]{54}\) be expressed as a product of smaller cube roots?
4. How do cube roots differ from square roots in terms of operations?
5. What is the cube root of 125?

**Tip:** When working with cube roots, remember that \(\sqrt[3]{a \times b} = \sqrt[3]{a} \times \sqrt[3]{b}\), which can sometimes make simplifying easier!

Learn how to simplify the expression -∛16 - 4∛54. This step-by-step solution covers cube roots and algebraic expressions, helping students understand the process of breaking down cube roots into simpler terms. Suitable for Grades 8-10.

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