What is the half of the number $2^{12}+3 \times 2^{10}$?
(a) $2^{6}+3 \times 2^{5}$
(b) $2^{6}+3 \times 2^{10}$
(c) $2^{1} 1+3 \times 2^{5}$
(d) $2^{11} \times 7$
(e) $2^{9} \times 7$
The correct option is (e).

Before dividing the expression by 2, we factor out $2^{10}$, obtaining $2^{12}+3 \times 2^{10}=2^{10}\left(2^{2}+3 \times 1\right)=2^{10} \times 7$. Thus,

$$
\frac{2^{12}+3 \times 2^{10}}{2}=\frac{2^{10} \times 7}{2}=2^{9} \times 7
$$