$$4x^{3}y^{6}\times3x^{3}y^{4}$$
$12x^{6}y^{10}$
$$4^{1}x^{3}y^{6}\times 3^{1}x^{3}y^{4}$$
$$4^{1}\times 3^{1}x^{3}x^{3}y^{6}y^{4}$$
$$4^{1}\times 3^{1}x^{3+3}y^{6+4}$$
$$4^{1}\times 3^{1}x^{6}y^{6+4}$$
$$4^{1}\times 3^{1}x^{6}y^{10}$$
$$12x^{6}y^{10}$$
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$72x^{5}y^{10}$
