Question

急求！两道高一指数幂运算题的答案！

1. x^(-1/2) + x^1/2 =3，求① x^(-2/3) + x^2/3 的值 ② x^(-3) + x^3 的值
2.若5^m =4，5^n =3 ，求5^ 2m-4n/3的值 （注：2m-4n 为一整体除以3。。2m-4n/3都是指数）
我需要过程，请写清楚，谢谢！

Answer 1

(1)①x+x^(-1)= [x^(-1/2) + x^1/2]²-2=7
∴x^(-2/3) + x^2/3=[x+x^(-1)]*[x^(-1/2) + x^1/2]- [x^(-1/2) + x^1/2]
=7*3-3
=18
② x^(-3) + x^3=x^[(-2/3) + x^2/3]²-2=322
（2）5^ （2m-4n）/3
=5^（2m/3)÷5^(4n/3)
=(5^m)^(2/3)÷(5^n)^(4/3)
=4^(2/3)÷3^(4/3)
=(2/3)^(4/3)