10^a=2,10^b=3,则100^[(3a/2)-(b/3)]=?

问题描述:

10^a=2,10^b=3,则100^[(3a/2)-(b/3)]=?

100^[(3a/2)-(b/3)] =10^{2[(3a/2)-(b/3)]} =10^[3a-(2b/3)] =10^(3a)/10^(2b/3) =(10^a)^3/(10^b)^(2/3) =2^3/(3)^(2/3) =8/9^(1/3)