计算：1、3xy³ × （-1/2x³y四次方）÷（-1/6x²y³）²

题目

计算：1、3xy³ × （-1/2x³y四次方）÷（-1/6x²y³）²
2、（a-1/2）²（a²+1/4）²（a+1/2）² 3、（1/3a²-1/4 b）（-1/4b-1/3 a平方）

答案

1、3xy^3 × (-1/2x^3y^4)÷(-1/6x^2y^3)^2
=3xy^3 × (-1/2x^3y^4)÷(-1/6x^2y^3)^2
=-3xy^3 × (1/2x^3y^4)÷(1/36x^4y^6)
=-(3×1/2÷1/36)x^(1+3-4)y^(3+4-6)
=-(3×1/2×36)x^0y
=-54y
2、(a-1/2)^2(a^2+1/4)^2(a+1/2)^2
=(a-1/2)^2(a+1/2)^2(a^2+1/4)^2
=[(a-1/2)(a+1/2)]^2(a^2+1/4)^2
=(a^2-1/4)^2(a^2+1/4)^2
=[(a^2-1/4)(a^2+1/4)]^2
=(a^4-1/16)^2
=a^8-a^4/8+1/256
3、(1/3a^2-1/4 b)(-1/4b-1/3 a^2)
=-(1/3a^2-1/4 b)(1/3 a^2+1/4b)
=-[(1/3a^2)^2-(1/4 b)^2]
=-(a^4/9- b^2/16)
=-a^4/9+b^2/16