1. Stating the problem: Simplify the expression $$\frac{25t}{7u} \times \frac{14}{15t}$$. 2. Write the expression as a single fraction: $$\frac{25t}{7u} \times \frac{14}{15t} = \frac{25t \times 14}{7u \times 15t}$$. 3. Multiply numerators and denominators: $$\frac{350t}{105ut}$$. 4. Cancel common factors: both numerator and denominator have $t$, so $$\frac{\cancel{350} \cancel{t}}{\cancel{105} u \cancel{t}} = \frac{350}{105} \times \frac{1}{u}$$. 5. Simplify the fraction $\frac{350}{105}$ by dividing numerator and denominator by 35: $$\frac{\cancel{350}^{10}}{\cancel{105}^{3}} = \frac{10}{3}$$. 6. Final simplified expression: $$\frac{10}{3u}$$. Therefore, the simplified form of the expression is $$\frac{10}{3u}$$.