$$\frac{4^{2}\times9^{2}\times3^{2}}{2^{2}\times6^{2}}$$
$81$
$$\frac{16\times 9^{2}\times 3^{2}}{2^{2}\times 6^{2}}$$
$$\frac{16\times 81\times 3^{2}}{2^{2}\times 6^{2}}$$
$$\frac{1296\times 3^{2}}{2^{2}\times 6^{2}}$$
$$\frac{1296\times 9}{2^{2}\times 6^{2}}$$
$$\frac{11664}{2^{2}\times 6^{2}}$$
$$\frac{11664}{4\times 6^{2}}$$
$$\frac{11664}{4\times 36}$$
$$\frac{11664}{144}$$
$$81$$
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$3^{4}$