To rewrite the irrational cube root \(-24\sqrt{3}\) as a product of an integer and another irrational cube root, we can factor \(-24\) as follows:
\[ -24 = -8 \times 3 \]
Next, we can express \(-24\sqrt{3}\) using this factorization:
\[ -24\sqrt{3} = (-8)(\sqrt{3}) = -8\sqrt{3} \]
Now, since \( -8 \) can be rewritten as \( -2^3 \), we can express \(-8\) in terms of its cube root:
\[ \sqrt[3]{-8} = -2 \]
Thus:
\[ -24\sqrt{3} = (-2)^3 \times \sqrt{3} = -2 \cdot \sqrt[3]{3 \cdot 8} = -2 \sqrt[3]{24} \]
However, to match the options provided, we realize we want to express \(-24\sqrt{3}\) in the simplest form related to the cube root:
Factoring out the cube root, we can say:
\[ -24\sqrt{3} = -2 \cdot \sqrt[3]{12 \cdot 3} = -2 \cdot \sqrt[3]{36} \]
Thus, the most suitable option corresponding to our simplified form is:
−2 \sqrt[3]{4}
(However, the original direct terms might ensure changes based on different constraints; options can't be fully validated as they require examining structured format.)