$$((4+4)^{2}\times6)+3-3^{2}$$
$378$
$$8^{2}\times 6+3-3^{2}$$
$$64\times 6+3-3^{2}$$
$$384+3-3^{2}$$
$$387-3^{2}$$
$$387-9$$
$$378$$
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$2\times 3^{3}\times 7$