1.若（a^n*b^m*b)³=a^9*b^15,求2^m+n的值.2.计算；a^n-5(a^n+1*b^3m-2)²+(a^n-1*b^m-2)³（-b^3m+2).3.若x=3a^n,y=-1/2*a^2n-1,当a=2,n=3时,求a^n*x-a*y的值.4.若2^x=4^y+1,27^y=3^x-1,求x-y的值.5.计算：（a-b)^m+3*(b-a)²*

Question

1.若（a^n*b^m*b)³=a^9*b^15,求2^m+n的值.
2.计算；a^n-5(a^n+1*b^3m-2)²+(a^n-1*b^m-2)³（-b^3m+2).
3.若x=3a^n,y=-1/2*a^2n-1,当a=2,n=3时,求a^n*x-a*y的值.
4.若2^x=4^y+1,27^y=3^x-1,求x-y的值.
5.计算：（a-b)^m+3*(b-a)²*(a-b)^m*(b-a)^5.

Answer 1

1.由（a^n*b^m*b)³=a^9*b^15可知,3n=9,3(m+1)=15,解得n=3,m=4
所以,2^m+n=2^7=128
2.a^n-5(a^n+1*b^3m-2)²+(a^n-1*b^m-2)³（-b^3m+2)
=(a^3n-3*b^6m-4)-(a^3n-3*b^6m-4)=0
3.当a=2,n=3时,有x=3a^n=24,y=-1/2*a^2n-1=16
所以,a^n*x-a*y=192-32=160
4.2^x=4^y+1,27^y=3^x-1,即2^x=2^2y+2,3^3y=3^x-1
因此有：x=2y+2,3y=x-1解得：x=4,y=1
所以,x-y=3
5.(a-b)^m+3*(b-a)²*(a-b)^m*(b-a)^5
=-(a-b)^m+3*(a-b)²*(a-b)^m*(a-b)^5
=-(a-b)^2m+10