已知a^3m=3,b^3n=2,求(a^2m)^3+(b^n)^3-a^2m·b^n·a^4m·b^2n的值.

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已知a^3m=3,b^3n=2,求(a^2m)^3+(b^n)^3-a^2m·b^n·a^4m·b^2n的值.

已知a^3m=3,b^3n=2,求(a^2m)^3+(b^n)^3-a^2m·b^n·a^4m·b^2n的值.
已知a^3m=3,b^3n=2,求(a^2m)^3+(b^n)^3-a^2m·b^n·a^4m·b^2n的值.

已知a^3m=3,b^3n=2,求(a^2m)^3+(b^n)^3-a^2m·b^n·a^4m·b^2n的值.
因为(a^2m)^3=(a^3m)^2=3^2=9,(b^n)^3=b^3n=2,a^2m·b^n·a^4m·b^2n=a^2m·a^4m·b^n·b^2n=a^(2m+4m)·b^(n+2n)=a^6m·b^3n=(a^3m)^2·b^3n=3^2·2=18,所以原式=9+2-18=-7

已知a^3m=3,b^3n=2,
(a^2m)^3+(b^n)^3-a^2m·b^n·a^4m·b^2n=(a^3m)^2+b^3n-a^(2m+4m)·b^(n+2n)=3^2+2-(3^2)·2=9+2-9*2=-7