Question
Evaluate: $\left[\left(\frac{5}{6}\right)^2 \times \frac{9}{4}\right] \div\left[\left(-\frac{3^2}{2}\right) \times \frac{125}{216}\right]$
✓
Answer
$\begin{aligned} & {\left[\left(\frac{5}{6}\right)^2 \times \frac{9}{4}\right] \div\left[\left(-\frac{3^2}{2}\right) \times \frac{125}{216}\right]} \\ & =\left[\frac{5 \times 5}{6 \times 6} \times \frac{9}{4}\right] \div\left[\frac{-3 \times-3}{2 \times 2} \times \frac{125}{216}\right] \\ & =\left[\frac{25}{36} \times \frac{9}{4}\right] \div\left[\frac{9}{4} \times \frac{125}{216}\right] \\ & =\left[\frac{25}{4} \times \frac{1}{4}\right] \div\left[\frac{1}{4} \times \frac{125}{24}\right] \\ & =\left[\frac{25}{16}\right] \div\left[\frac{125}{96}\right] \\ & =\frac{25}{16} \times \frac{96}{125} \\ & =\frac{1}{1} \times \frac{6}{5}=1 \frac{1}{5}\end{aligned}$
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