(a^m+1乘以b^n+2)乘以（a^2n-1乘以b^2m）=a^5b^3,则m+n的值为多少？要有过程，详细一点

Question

要有过程，详细一点

Answer 1

a(^m+1乘以b^n+2)乘以（a^2n-1乘以b^2m）=a^5b^3,
[a^(m+1)*b^(n+2)]*[a^(2n-1)*b^(2m）]=a^5b^3,
[a^(m+1)*a^(2n-1)][b^(n+2)*b^(2m）]=a^5b^3,
a^(m+1+2n-1)*b^(n+2+2m）=a^5b^3,
a^(m+2n)*b^(n+2+2m）=a^5b^3,
有下列方程组：
m+2n=5
2m+n+2=3
即
m+2n=5
2m+n=1
两式相加：
3m+3n=6
3(m+n)=6
m+n=6/3=2.