Question

已知5 x的3n+5次方y的3m-1次方÷（-5x的n+1次方y的m次方）的2次方=五分之一 x的2次方y的2次方,求m

Answer 1

5x^(3n+5)y^(3m-1)÷[-5x^(n+1)y^m]^2=1/5x^(2)y^2

5x^(3n+5)y^(3m-1)÷25x^(2n+2)y^2m=1/5x^(2)y^2

1/5x^(3n+5-2n-2)y^(3m-1-2m)=1/5x^(2)y^2

1/5x^(n+3)y^(m-1)=1/5x^(2)y^2

那么n+3=2,m-1=2,所以n=-1,m=3将此代入上式中.

m^n-1=3^-1-1=3^-2=1/9