$$(\frac{3}{4})^{-2}\div(\frac{4}{9})^{3}\times\frac{16}{27}$$
$12$
$$\frac{\frac{16}{9}}{\left(\frac{4}{9}\right)^{3}}\times \frac{16}{27}$$
$$\frac{\frac{16}{9}}{\frac{64}{729}}\times \frac{16}{27}$$
$$\frac{16}{9}\times \frac{729}{64}\times \frac{16}{27}$$
$$\frac{81}{4}\times \frac{16}{27}$$
$$12$$
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$2^{2}\times 3$
