1. (3 points) The value of the expression $10-10.5 \div[5.2 \times 14.6-(9.2 \times 5.2+5.4 \times 3.7-4.6 \times 1.5)]$ is
【Analysis】10-10.5 $\div[5.2 \times 14.6-(9.2 \times 5.2+5.4 \times 3.7-4.6 \times 1.5)]$ First remove the parentheses to become 10 $-10.5 \div[5.2 \times 14.6-9.2 \times 5.2-5.4 \times 3.7+4.6 \times 1.5]$, use the distributive law of multiplication to become $10-10.5 \div$ $[5.2 \times(14.6-9.2)-5.4 \times 3.7+4.6 \times 1.5]$, then use the distributive law of multiplication to become $5.2 \times 5.4-5.4 \times 3.7+4.6$ $\times 1.5$, and use the distributive law of multiplication again for simplification.

【Solution】Solution: $10-10.5 \div[5.2 \times 14.6-(9.2 \times 5.2+5.4 \times 3.7-4.6 \times 1.5)]$,
$$
\begin{array}{l}
=10-10.5 \div[5.2 \times 14.6-9.2 \times 5.2-5.4 \times 3.7+4.6 \times 1.5], \\
=10-10.5 \div[5.2 \times(14.6-9.2)-5.4 \times 3.7+4.6 \times 1.5], \\
=10-10.5 \div[5.2 \times 5.4-5.4 \times 3.7+4.6 \times 1.5], \\
=10-10.5 \div[5.4 \times(5.2-3.7)+4.6 \times 1.5], \\
=10-10.5 \div[5.4 \times 1.5+4.6 \times 1.5], \\
=10-10.5 \div[1.5 \times(5.4+4.6)], \\
=10-10.5 \div 15 \\
=10-0.7 \\
=9.3 .
\end{array}
$$

Therefore, the answer is: 9.3 .