Question

数学指数式化简 （字母均为正数）要详细过程 在线等 急！！！谢谢

1>> (5/6)a^(1/3)*b(-2)*[-3a^(-1/2)b^(-1)]除以[4a^(2/3)*b(-3)]^1/2

2>> (a^1/2-b^1/2)/(a^1/2+b^1/2)+ (a^1/2+b^1/2)/(a^1/2-b^1/2)

Answer 1

1>> (5/6)a^(1/3)*b^(-2)*[-3a^(-1/2)b^(-1)]除以[4a^(2/3)*b^(-3)]^(1/2)
= (5/6)*(-3)a^(1/3-1/2)*b^(-2-1)除以[4^(1/2)a^((2/3)*(1/2))b^((-3)*(1/2))]
=(-5/2)a^(-1/6)b^(-3)除以[2a^((1/3)b^((-3/2))]
=(-5/2)/2a^(-1/6-1/3)b^(-3-(-3/2))
=(-5/4)a^(-1/2)b^(-3/2)
2>> (a^1/2-b^1/2)/(a^1/2+b^1/2)+ (a^1/2+b^1/2)/(a^1/2-b^1/2)
=(a^1/2-b^1/2)^2/(a-b)+ (a^1/2+b^1/2)^2/(a-b)
=((a^1/2-b^1/2)^2+ (a^1/2+b^1/2)^2)/(a-b)
=(a-2a^1/2b^1/2+b+a +2a^1/2^1/2+b)/(a-b)
=2(a+b)/(a-b)

Answer 2

(5/6)a^(1/3)*b(-2)*[-3a^(-1/2)b^(-1)]除以[4a^(2/3)*b(-3)]^1/2=-5/8a^1/2b(-3/2)
(a^1/2-b^1/2)/(a^1/2+b^1/2)+ (a^1/2+b^1/2)/(a^1/2-b^1/2)=2a-2b

Answer 3

(5/6)a^(1/3)*b(-2)*[-3a^(-1/2)b^(-1)]/{[4a^(2/3)*b(-3)]^1/2}
=(5/6)a^(1/3)*b(-2)*(-3/4)a^[(-1/2)b^(-1)-(2/3)]*(-3b)^(-1/2)
=(5/4)*a^[(-1/3)-(1/2)b^(-1)]*(-3b)^(-1/2)*b

(a^1/2-b^1/2)/(a^1/2+b^1/2)+ (a^1/2+b^1/2)/(a^1/2-b^1/2)
=[(a^1/2-b^1/2)*(a^1/2-b^1/2)]/[ (a^1/2+b^1/2)*(a^1/2-b^1/2)]+
[(a^1/2+b^1/2)*(a^1/2+b^1/2)]/(a^1/2-b^1/2)*(a^1/2+b^1/2)]
=[a+b-(1/2)a^(1/2)*b^(1/2)]/(a-b)]+[a+b+(1/2)a^(1/2)*b^(1/2)]/(a-b)
=(2a+2b)/(a-b)