Respuesta:
[tex]\frac{15}{64}[/tex]
Explicación paso a paso:
[tex]\left(\frac{13}{8}\cdot \frac{5}{65}\right)\div \left(3\frac{1}{5}-2\frac{2}{3}\right)\\\\3\frac{1}{5}\\\\3\frac{1}{5}=\frac{3\cdot 5+1}{5}\\\\=\frac{16}{5}\\\\=\left(\frac{13}{8}\cdot \frac{5}{65}\right)\div \left(\frac{16}{5}-2\frac{2}{3}\right)\\\\2\frac{2}{3}\\\\2\frac{2}{3}=\frac{2\cdot 3+2}{3}\\\\=\frac{8}{3}\\\\=\left(\frac{13}{8}\cdot \frac{5}{65}\right)\div \left(\frac{16}{5}-\frac{8}{3}\right)\\\\\frac{1}{13}\\\\[/tex]
[tex]\left(\frac{13}{8}\cdot \frac{1}{13}\right)\div \left(\frac{16}{5}-\frac{8}{3}\right)\\\\\frac{13}{8}\cdot \frac{1}{13}\\\\=\frac{1}{8}\\\\=\frac{1}{8}\div \left(\frac{16}{5}-\frac{8}{3}\right)\\\\\frac{16}{5}-\frac{8}{3}\\\\=\frac{48}{15}-\frac{40}{15}\\\\=\frac{48-40}{15}\\\\=\frac{8}{15}\\\\=\frac{1}{8}\div \frac{8}{15}\\\\=\frac{1}{8}\cdot \frac{15}{8}\\\\=\frac{1\cdot \:15}{8\cdot \:8}\\\\=\frac{15}{64}[/tex]
