The given image shows the mathematical expression:

$\sqrt[3]{-64}$

This represents the cube root of $-64$. To solve this, we need to find a number that, when multiplied by itself three times, equals $-64$.

We know:

$(-4) \times (-4) \times (-4) = -64$

So:

$\sqrt[3]{-64} = -4$

The answer is $-4$.

Would you like a more detailed explanation or have any additional questions? Here are some related questions you could explore:

1. What is the cube root of a positive number, like $64$?
2. How do cube roots differ from square roots for negative numbers?
3. Can you take the even root (e.g., square root) of a negative number?
4. What are imaginary numbers and how do they relate to negative square roots?
5. How can cube roots be calculated using a calculator or manually?

Tip: Cube roots of negative numbers always result in a negative value, since multiplying an odd number of negative factors results in a negative product.