（1）(214)12−(−9.6)0−(338)−23+(1.5)−2；（2）已知2a=5b=m，且1a+1b＝2，求m的值．

Question

（1）(2(1)/(4))(1)/(2)−(−9.6)0−(3(3)/(8))−(2)/(3)+(1.5)−2；
（2）已知2^a=5^b=m，且(1)/(a)+(1)/(b)＝2，求m的值．

Answer 1

（1）(2(1)/(4))(1)/(2)−(−9.6)0−(3(3)/(8))−(2)/(3)+(1.5)−2
=((9)/(4))(1)/(2)−1−((27)/(8))−(2)/(3)+((3)/(2))−2
=(3)/(2)−1−(((2)/(3))3)(2)/(3)+((2)/(3))2
=(1)/(2)−(4)/(9)+(4)/(9)
=(1)/(2)．
（2）由2^a=5^b=m，得：a=log₂m，b=log₅m．
再由(1)/(a)+(1)/(b)＝2，得：(1)/(log2m)+(1)/(log5m)＝logm2+logm5=log_m10=2，
所以，m²=10，m=√(10)．