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