6.18 If $60^{a}=360^{b}=5$, then $12^{\frac{1-a-b}{2(1-b)}}$ is
(A) $\sqrt{3}$.
(B) 2.
(C) $\sqrt{5}$.
(D) 3.
(E) $\sqrt{12}$.
(34th American High School Mathematics Examination, 1983)
[Solution] From $12=\frac{60}{5}=\frac{60}{60^{b}}=60^{1-b}$, we have
$$
12^{\frac{1-a-b}{2(1-b)}}=\left[60^{1-b}\right]^{\frac{1-a-b}{2(1-b)}}=60^{\frac{1-a-b}{2}}=\sqrt{\frac{60}{60^{a} 60^{b}}}=\sqrt{\frac{60}{3 \cdot 5}}=2 \text{. }
$$

Therefore, the answer is $(B)$.