Question

化简求值：（3/4a^4b^7+1/18a^3b^8-1/9a^2b^6）÷（-1/3ab^3）^2,其中a=1/2，b=-4

Answer 1

（3/4a^4b^7+1/18a^3b^8-1/9a^2b^6）÷（-1/3ab^3）^2
=（3/4a^4b^7+1/18a^3b^8-1/9a^2b^6）÷(-1/9a^2b^6)
=3/4a^4b^7÷(-1/9a^2b^6)+1/18a^3b^8÷(-1/9a^2b^6)-1/9a^2b^6÷(-1/9a^2b^6)
=-27/4a^2b-1/2ab^2+1
=27/4-4+1
=15/4

Answer 2

（3/4a^3+1/2a^3b^3-1/9a^2b^4）/(-1/3ab)^2
=(a^2/36)（27a+18ab^3-4b^4）/(1/9a^2b^2)
=(27a+18ab^3-4b^4）/4b^2
=27a/4b^2+9ab/2-b^2
=27*(1/2)/4*(-4)^2+9*(1/2)*4/2-(-4)^2
=27/128-7
=-869/128