The problem displayed is the cube root of $-0.125$, denoted as:

$\sqrt[3]{-0.125}$

Unlike square roots, cube roots of negative numbers do exist in the real number system. The cube root of $-0.125$ is calculated as follows:

1. $-0.125$ is equivalent to $-\frac{1}{8}$.
2. The cube root of $\frac{1}{8}$ is $\frac{1}{2}$.
3. Therefore, the cube root of $-\frac{1}{8}$ is $-\frac{1}{2}$.

Thus, the correct answer is:

$\sqrt[3]{-0.125} = -\frac{1}{2}$

The given response of "no real solution" is incorrect because there is indeed a real solution.

Would you like more details or have any questions?

Here are some related questions you might consider:

1. What is the difference between square roots and cube roots of negative numbers?
2. How do you calculate cube roots of decimals?
3. What are the properties of cube roots in terms of negative and positive numbers?
4. How would you simplify the cube root of a fraction?
5. How does the cube root function differ from other radical functions?

Tip: Cube roots of negative numbers always result in negative real numbers, unlike square roots.