Evaluate. \[ \left[\left(1 \frac{1}{4}-\frac{3}{4}\right) \cdot\left(-\frac{2}{3}\right)^{3}\right] \div(-4) \] What is the value of the expression? Enter your answer as a simplified fractio

Step 1 ：Convert the mixed number \(1 \frac{1}{4}\) to an improper fraction. The result is \(\frac{5}{4}\).

Step 2 ：Subtract \(\frac{3}{4}\) from \(\frac{5}{4}\) to get \(\frac{1}{2}\).

Step 3 ：Raise \(-\frac{2}{3}\) to the power of 3 to get \(-\frac{8}{27}\).

Step 4 ：Multiply \(\frac{1}{2}\) by \(-\frac{8}{27}\) to get \(-\frac{4}{27}\).

Step 5 ：Divide \(-\frac{4}{27}\) by \(-4\) to get \(\frac{1}{27}\).

Step 6 ：Final Answer: The value of the expression is \(\boxed{\frac{1}{27}}\).