已知（ab²）的m次方·（3a的m次方·b的n-1次方）²=b（ab²）的n次方·（3a的m次方1b）²,求m+n的值

题目

已知（ab²）的m次方·（3a的m次方·b的n-1次方）²=b（ab²）的n次方·（3a的m次方1b）²,求m+n的值

答案

((ab)^2)^m*((3a)^m*b^(n-1))^2=(b(ab^2))^n*(((3a)^m)^2*b)^2
left=(ab)^(2m)*(3a)^(2m)*b^(2n-2)=3^(2m)*a^(2m+2m)*b^(2n-2+2m)=3^(2m)*a^(4m)*b^(2n+2m-2)
right=3^(2m)*a^(2m+n+2m)*b^(n+2n+2)=3^(2m)*a^(4m+n)*b^(3n+2)
4m=4m+n,2n+2m-2=3n+2,
n=0,m=2
m+n=2