The problem is to rationalize the denominator of the expression $\frac{-2}{\sqrt[3]{15}}$.

1. Problem Description

The problem is to rationalize the denominator of the expression $\frac{-2}{\sqrt[3]{15}}$.

2. Solution Steps

To rationalize the denominator, we need to eliminate the cube root from the denominator. To do this, we will multiply both the numerator and the denominator by a factor that will make the expression inside the cube root a perfect cube.

We have $\frac{-2}{\sqrt[3]{15}}$.

We need to multiply the denominator $\sqrt[3]{15}$ by $\sqrt[3]{15^2}$ to obtain $\sqrt[3]{15^3} = 15$.

So, we multiply the numerator and denominator by $\sqrt[3]{15^2}$:

$\frac{-2}{\sqrt[3]{15}} \cdot \frac{\sqrt[3]{15^2}}{\sqrt[3]{15^2}} = \frac{-2\sqrt[3]{15^2}}{\sqrt[3]{15^3}} = \frac{-2\sqrt[3]{225}}{15}$.

3. Final Answer

The expression with a rationalized denominator is $\frac{-2\sqrt[3]{225}}{15}$.