$$(\frac{2}{3})^{5}\div(\frac{2}{3})^{8}\times(\frac{2}{3})^{3}$$
$1$
$$\frac{1}{\left(\frac{2}{3}\right)^{3}}\times \left(\frac{2}{3}\right)^{3}$$
$$\frac{1}{\frac{8}{27}}\times \left(\frac{2}{3}\right)^{3}$$
$$1\times \frac{27}{8}\times \left(\frac{2}{3}\right)^{3}$$
$$\frac{27}{8}\times \left(\frac{2}{3}\right)^{3}$$
$$\frac{27}{8}\times \frac{8}{27}$$
$$1$$
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