$$[(\frac{81}{16})^{-3/4}\times(\frac{25}{9})^{-3/2}\div(\frac{5}{2})^{-3}]$$
$1$
$$\frac{\left(\frac{81}{16}\right)^{-\frac{3}{4}}\times \left(\frac{25}{9}\right)^{\frac{-3}{2}}}{\left(\frac{5}{2}\right)^{-3}}$$
$$\frac{\frac{8}{27}\times \left(\frac{25}{9}\right)^{\frac{-3}{2}}}{\left(\frac{5}{2}\right)^{-3}}$$
$$\frac{\frac{8}{27}\times \left(\frac{25}{9}\right)^{-\frac{3}{2}}}{\left(\frac{5}{2}\right)^{-3}}$$
$$\frac{\frac{8}{27}\times \frac{27}{125}}{\left(\frac{5}{2}\right)^{-3}}$$
$$\frac{\frac{8}{125}}{\left(\frac{5}{2}\right)^{-3}}$$
$$\frac{\frac{8}{125}}{\frac{8}{125}}$$
$$1$$
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