Question

求解两道指数函数化简题：化简下列各式

Answer 1

(1).[x^(-2)+y^(-2)] / [x^(-2/3)+y^(-2/3)] - [x^(-2)-y^(-2)] / [x^(-2/3)-y^(-2/3)]

= {[x^(-2)+y^(-2)] [x^(-2/3)-y^(-2/3)] - [x^(-2)-y^(-2)] [x^(-2/3)+y^(-2/3)]}/

[x^(-4/3)-y^(-4/3)]

= 2x^(-2/3)y^(-2/3)[y^(-4/3)-x^(-4/3)/[x^(-4/3)-y^(-4/3)]

= -2/(xy)^(2/3).

(2) [a^3+a^(-3)] [a^3-a^(-3)] / {[a^4+a^(-4)+1] [a-a^(-1)]}

= [a^3+a^(-3)] [a^2+1+a^(-2)] / [a^4+a^(-4)+1]

= (a^6+1) (a^4+a^2+1) / [a(a^8+a^4+1)]

= (a^2+1) (a^4-a^2+1)(a^4+a^2+1) / [a(a^8+a^4+1)]

= (a^2+1) [(a^4+1)^2-a^4]/ [a(a^8+a^4+1)]

= (a^2+1)/a = a+a^(-1).