1. The problem asks to write $-\frac{2}{3} \sqrt{5}$ as a single radical expression. 2. Recall that a fractional coefficient can be expressed inside a radical by using the property $a \sqrt{b} = \sqrt{a^2 b}$ if $a$ is rational. 3. Here, $-\frac{2}{3} \sqrt{5}$ can be rewritten as $-\sqrt{\left(\frac{2}{3}\right)^2 \times 5}$. 4. Calculate $\left(\frac{2}{3}\right)^2 = \frac{4}{9}$. 5. Substitute back: $-\sqrt{\frac{4}{9} \times 5} = -\sqrt{\frac{20}{9}}$. 6. Simplify the radical: $-\sqrt{\frac{20}{9}} = -\frac{\sqrt{20}}{3}$. 7. Since $\sqrt{20} = \sqrt{4 \times 5} = 2 \sqrt{5}$, substitute to get $-\frac{2 \sqrt{5}}{3}$. 8. This matches the original expression, confirming the single radical form is $-\sqrt{\frac{20}{9}}$. Final answer: $$-\sqrt{\frac{20}{9}}$$