解:(1)19×8×125,
=19×(8×125),
=19×1000,
=19000;
(2)38+129+71,
=38+(129+71),
=38+200,
=238;
(3)1900÷4÷25,
=1900÷(4×25),
=1900÷100,
=19;
(4)99×78+80,
=99×78+78+2,
=(99+1)×78+2,
=100×78+2,
=7800+2,
=7802.
分析:(1)19×8×125,运用乘法结合律进行简算;
(2)38+129+71,运用加法结合律进行简算;
(3)1900÷4÷25,根据除法的运算性质进行简算;
(4)99×78+80,将原式转化为:99×78+78+2,然后运用乘法分配律进行简算.
点评:此题考查的目的灵活运用加法、乘法的运算定律和除法的运算性质进行简便计算.