To rewrite $\sqrt[3]{128}$ (the cube root of 128) in its simplest form, follow these steps:

1. Prime Factorization of 128: $128 = 2^7$

2. Cube Roots: We look for groups of three identical factors, as that's what a cube root simplifies: [ \sqrt[3]{2^7} = \sqrt[3]{2^6 \times 2} = 2^2 \times \sqrt[3]{2} = 4\sqrt[3]{2} ]

So, $\sqrt[3]{128} = 4\sqrt[3]{2}$.

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Here are 5 related questions:

1. What is the cube root of 64?
2. How do you simplify cube roots involving prime numbers?
3. What is the cube root of 343?
4. How do you handle cube roots for non-perfect cubes?
5. How is cube root simplification different from square root simplification?

Tip: Always factor numbers fully to spot cubes or squares when simplifying roots.