The expression in the image is:

[ 2 \sqrt[3]{4} \left( \sqrt[3]{2} + \sqrt[3]{16} \right) ]

Let's break it down step by step:

1. Evaluate each cube root:

   • $\sqrt[3]{4} \approx 1.5874$
   • $\sqrt[3]{2} \approx 1.2599$
   • $\sqrt[3]{16} = \sqrt[3]{2^4} = 2 \sqrt[3]{2} \approx 2 \times 1.2599 = 2.5198$

2. Simplify the terms inside the brackets: [ \sqrt[3]{2} + \sqrt[3]{16} \approx 1.2599 + 2.5198 = 3.7797 ]

3. Multiply by $2 \sqrt[3]{4}$: $2 \times 1.5874 \times 3.7797 \approx 12.003$

Thus, the simplified value of the expression is approximately $12$.

Would you like a detailed breakdown of any part, or do you have further questions?

Here are five related questions for further exploration:

1. What is the general process for evaluating cube roots of non-perfect cubes?
2. How would this calculation change if the exponent was a square root instead of a cube root?
3. Can this expression be rewritten using fractional exponents?
4. What happens if you cube the result to reverse the operations?
5. How does the calculation differ if the constants were inside the cube root?

Tip: When working with cube roots, it can be helpful to approximate the values of small numbers or express them using known powers for more precision.