Answer
-7
Work Step by Step
$\sin 90^{\circ}=1$
$\cos 180^{\circ}=-1$
$\implies$
$-3\sin^{4} 90^{\circ}+4\cos^{3}180^{\circ}=$
$-3(1)^{4}+4(-1)^{3}=-3-4=-7$
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