[Solution] (1),(3) are correct;
For (2), by $\frac{a^{6} x^{6}}{-a x^{3}}=-a^{5} x^{3}$, we know (2) is wrong;
For (4), by $\left[(-3)^{m}\right]^{2}=(-3)^{2 m}=3^{2 m}=\left(3^{m}\right)^{2}$, we know (4) is wrong. Therefore, the answer is $(B)$.
6.2 Below are four problems solved by a student:
(1) $6 a^{\frac{2}{3}} \times 7 a^{\frac{1}{2}}=42 a^{1 \frac{1}{6}}$;
(2) $(-a x)^{6} \div\left(-a x^{3}\right)=a^{5} x^{3}$;
(3) $\left(-1989^{0}\right)^{1989}=-1$;
(4) $\left[(-3)^{m}\right]^{2}=3^{m^{2}}$.

The number of problems the student solved correctly is
(A) 1.
(B) 2.
(C) 3.
(D) 4.
(China Sichuan Junior High School Mathematics Competition, 1989)