$$\frac{(\frac{1}{2}\rfloor^{-8}\cdot(\frac{2}{3})^{-2}\cdot(\frac{9}{2})^{3}}{2^{3}\cdot(\frac{4}{9})^{-1}\cdot(\frac{1}{3})^{-3}\cdot(\frac{4}{3})^{2}}=$$
$\frac{81}{2}=40.5$
$$\frac{\left(\frac{1}{2}\right)^{-8}\times \left(\frac{2}{3}\right)^{-2}\times \left(\frac{9}{3}\right)^{3}}{2^{3}\times 1^{-1}\times \left(\frac{1}{3}\right)^{-3}\times \left(\frac{4}{3}\right)^{2}}$$
$$\frac{256\times \left(\frac{2}{3}\right)^{-2}\times \left(\frac{9}{3}\right)^{3}}{2^{3}\times 1^{-1}\times \left(\frac{1}{3}\right)^{-3}\times \left(\frac{4}{3}\right)^{2}}$$
$$\frac{256\times \frac{9}{4}\times \left(\frac{9}{3}\right)^{3}}{2^{3}\times 1^{-1}\times \left(\frac{1}{3}\right)^{-3}\times \left(\frac{4}{3}\right)^{2}}$$
$$\frac{576\times \left(\frac{9}{3}\right)^{3}}{2^{3}\times 1^{-1}\times \left(\frac{1}{3}\right)^{-3}\times \left(\frac{4}{3}\right)^{2}}$$
$$\frac{576\times 3^{3}}{2^{3}\times 1^{-1}\times \left(\frac{1}{3}\right)^{-3}\times \left(\frac{4}{3}\right)^{2}}$$
$$\frac{576\times 27}{2^{3}\times 1^{-1}\times \left(\frac{1}{3}\right)^{-3}\times \left(\frac{4}{3}\right)^{2}}$$
$$\frac{15552}{2^{3}\times 1^{-1}\times \left(\frac{1}{3}\right)^{-3}\times \left(\frac{4}{3}\right)^{2}}$$
$$\frac{15552}{8\times 1^{-1}\times \left(\frac{1}{3}\right)^{-3}\times \left(\frac{4}{3}\right)^{2}}$$
$$\frac{15552}{8\times 1\times \left(\frac{1}{3}\right)^{-3}\times \left(\frac{4}{3}\right)^{2}}$$
$$\frac{15552}{8\times \left(\frac{1}{3}\right)^{-3}\times \left(\frac{4}{3}\right)^{2}}$$
$$\frac{15552}{8\times 27\times \left(\frac{4}{3}\right)^{2}}$$
$$\frac{15552}{216\times \left(\frac{4}{3}\right)^{2}}$$
$$\frac{15552}{216\times \frac{16}{9}}$$
$$\frac{15552}{384}$$
$$\frac{81}{2}$$
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$\frac{3 ^ {4}}{2} = 40\frac{1}{2} = 40.5$
