小女子感激不尽1.如果a^4+a=0,求a^（2005）+a^（2002）-12的值2.已知10^a=20,10^b=5^-1,求9^a÷3^2b的值3.计算：a^n-5(a^n+1b^3m-2)^2+(a^n-1b^m-2)^3(-b^3m+2)4.若2^x=4^y+1,27=3^x-1,求x-y的值5.若（a^m+1b^n+2)(a^2n-1b^2n)=a^

Question

小女子感激不尽 1.如果a^4+a=0,求a^（2005）+a^（2002）-12的值
2.已知10^a=20,10^b=5^-1,求9^a ÷3^2b的值
3.计算：a^n -5(a^n+1 b^3m-2)^2+(a^n-1 b^m-2)^3(-b^3m+2)
4.若2^x=4^y+1,27=3^x-1,求x-y的值
5.若（a^m+1 b^n+2)(a^2n-1 b^2n)=a^5 b^3,则求m+n的值
6.已知xy^2=-6,求-xy(x^3 y^7 -3x^2 y^5-y)

Answer 1

a^4+a=0,
a^（2005）+a^（2002）-12
=a^2001(a^4+a)-12
=0-12
=-12
2..已知10^a=20,10^b=5^-1
10^a=20,10^b=1/5
所以10^a/10^b=20/(1/5)
10^(a-b)=100
10^(a-b)=10^2
a-b=2
9^a ÷3^2b
=9^a/9^b
=9^(a-b)
=9^2
=81
3.计算：a^n -5(a^n+1 b^3m-2)^2+(a^n-1 b^m-2)^3(-b^3m+2)
=a^(n-5)*a^(2n+2)*b^(6m-4)+a^(3n-3)**b^(3m-6)*b^(3m+2)
=a^(3n-3)*b^(6m-4)+a^(3n-3)*b^(6m-4)
=2a^(3n-3)*b^(6m-4)
4.若2^x=4^y+1,27=3^x-1,求x-y的值
2^x=2^2(y+1) 3^3=3^x-1
x=2(y+1) 3=x-1
x=4 y=1
x-y=4-1=3
5.若（a^m+1 b^n+2)(a^2n-1 b^2n)=a^5 b^3,则求m+n的值
a^(m+1)*b^(n+2)*a^(2n-1)*b^2m
=a^(m+1+2n-1)*b^(n+2+2m)
=a^(m+2n)*b^(2m+n+2)
=a^3*b^5
所以
m+2n=3……①
2m+n+2=5……②
由2m+n+2=5可得2m+n=3……③
①+③可得
3(m+n)=6
所以m+n=2
6.已知xy^2=-6,求-xy(x^3 y^7 -3x^2 y^5-y)
原式=-x^4y^8+3x³y^6+xy²
=-(xy²)^4+3(xy²)³+xy²
=-1296-648-6
=-1950