解答:利用中间量0.2^0.2考察幂函数y=x^0.2在(0,+∞)上是增函数0.5>0.2∴ 0.5^0.2>0.2^0.2 -------①考察指数函数y=0.2^x在(0,+∞)上是减函数0.5>0.2∴ 0.2^0.2>0.2^0.5 ------②由①②, 0.5^0.2>0.2^0.5
0.5^0.2=(1/2)^(1/5)=1/(2开五次方)0.2^0.5=(1/5)^(1/2)=1/(5开平方)2开五次方<5开平方0.5^0.2>0.2^0.5