https://file.aiquickdraw.com/mathbot/file/17268421526790pxgh0dr.jpg

Let's break down the expression provided in the image:

The problem asks to find the difference:

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

### Step 1: Simplify the cube root of 16

We know that \(16 = 2^4\), so:

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

This is approximately \(2^{4/3} \approx 2.5198421\), but we'll leave it in exact form for now.

### Step 2: Set up the subtraction

We now have:

\[
5 \sqrt[3]{2} - 2^{4/3}
\]

To simplify further, observe that there are no like terms to combine since \(5 \sqrt[3]{2}\) and \(2^{4/3}\) are different kinds of expressions (the exponents do not match directly).

### Step 3: Approximate or match the correct answer

If you compute the approximate value:

- \(5 \sqrt[3]{2} \approx 5 \times 1.260 = 6.30\)
- \(2^{4/3} \approx 2.5198421\)

Thus:

\[
5 \sqrt[3]{2} - 2^{4/3} \approx 6.30 - 2.52 = 3.78
\]

### Step 4: Compare with the choices

The closest match to this result is:

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

### Final Answer: \(\boxed{3 \sqrt[3]{2}}\)

---

Do you need further details on this solution?

Here are 5 questions to expand on this topic:
1. How do you calculate higher roots like cube roots for larger numbers?
2. Why can't we simplify \(5 \sqrt[3]{2} - \sqrt[3]{16}\) directly without approximation?
3. How do you work with exponents like \(2^{4/3}\)?
4. What are some applications of cube roots in geometry and physics?
5. How do fractional exponents relate to radical expressions?

**Tip**: When dealing with cube roots, always check if you can express the numbers as powers of smaller prime numbers (like \(16 = 2^4\)) to make simplification easier.

This problem demonstrates how to find the difference between cube roots, specifically 5∛2 and ∛16. Simplify the cube root of 16 and calculate the subtraction step by step. Suitable for students in Grades 8-10.

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