Multiply or divide as indicated. Write answers in lowest terms as needed. $2\frac{2}{3}\cdot 1\frac{3}{5}$

First, convert the mixed numbers to improper fractions. For 2(2/3), multiply the whole number 2 by the denominator 3 and add the numerator 2: \(2 \times 3 + 2 = 8\), so \(2(2/3) = \frac{8}{3}\). For 1(3/5), multiply the whole number 1 by the denominator 5 and add the numerator 3: \(1 \times 5 + 3 = 8\), so \(1(3/5) = \frac{8}{5}\).