1. The problem is to simplify the expression $$\frac{2}{3} \times \frac{3}{2} \times q^{\frac{3}{2}}$$. 2. Recall the multiplication rule for fractions: $$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$$. 3. Multiply the fractions $$\frac{2}{3}$$ and $$\frac{3}{2}$$: $$\frac{2 \times 3}{3 \times 2} = \frac{6}{6} = 1$$. 4. Now the expression simplifies to: $$1 \times q^{\frac{3}{2}} = q^{\frac{3}{2}}$$. 5. Therefore, the simplified expression is $$q^{\frac{3}{2}}$$. This means the original expression simplifies to the power of $$q$$ raised to $$\frac{3}{2}$$.