To solve the expression \((8 \backslash 9) \times (-3 \backslash 4) \div (1 \backslash 9) \times (-4 \backslash 5) \div (3 \backslash 5)\), we first need to clarify what you mean by the symbol "\backslash." If we assume it denotes a fraction, we will rewrite it using the division notation.
Thus, we can translate the expression into fractions as follows:
\[ \frac{8}{9} \times \left(-\frac{3}{4}\right) \div \frac{1}{9} \times \left(-\frac{4}{5}\right) \div \frac{3}{5} \]
Now, we'll perform the calculations step by step:
- Calculate the first multiplication:
\[ \frac{8}{9} \times \left(-\frac{3}{4}\right) = -\frac{8 \times 3}{9 \times 4} = -\frac{24}{36} = -\frac{2}{3} \]
- Now we will divide this result by \(\frac{1}{9}\). Dividing by a fraction is the same as multiplying by its reciprocal:
\[ -\frac{2}{3} \div \frac{1}{9} = -\frac{2}{3} \times 9 = -2 \times 3 = -6 \]
- Next, we will multiply this result by \(-\frac{4}{5}\):
\[ -6 \times \left(-\frac{4}{5}\right) = \frac{24}{5} \]
- Finally, we will divide this result by \(\frac{3}{5}\):
\[ \frac{24}{5} \div \frac{3}{5} = \frac{24}{5} \times \frac{5}{3} = \frac{24 \times 5}{5 \times 3} = \frac{24}{3} = 8 \]
Thus, the final answer is:
\[ \boxed{8} \]