Question

已知（x^5m+n * y^2m-n)^3=x^6 * y^15,求n^m的值

Answer 1

[x^(5m+n) * y^(2m-n)]^3=x^6 * y^15

x^[3*(5m+n)]*y[3(2m-n)]=x^6 * y^15

x^(15m+3n)*y^(6m-3n)=x^6 * y^15

15m+3n=6

5m+n=2.1

6m-3n=15

2m-n=5.2

1式+2式得

7m=7

m=1

将m=1代入1式得

5m+n=2

5+n=2

n=-3

n^m

=(-3)^1

=-3