Question

已知x,y为正整数，且（16的x加1次方·27的x-1次方）÷（2的3y+2次方·3的2y-5次方）=18，试求x得y次方的值

Answer 1

（16的x加1次方·27的x-1次方）÷（2的3y+2次方·3的2y-5次方）
=(2^4)^(x+1)*(3^3)^(x-1)÷[2^(3y+2)*3^(2y-5)]
=2^(4x+4-3y-2)*3^(3x-3-2y+5)
=2^(4x-3y+2)*3^(3x-2y+2)
=18
=2*3^2
因x,y为正整数
所以4x-3y+2=1即4x-3y+1=0 (1)
3x-2y+2=2 即 3x-2y=0 (2)
(1)*2-(2)*3 -x+2=0 解得x=2
代入(2) y=3
所以x^y=2^3=8

Answer 2

[16^(x+1)*27^(x-1)]÷(2^(3y+2)*3^(2y-5)]=18
[(2^4)^(x+1)*(3^3)^(x-1)]÷[(2^(3y+2)*3^(2y-5)]=18
[2^(4x+4)*3^(3x-3)]÷[(2^(3y+2)*3^(2y-5)]=18
2^(4x+4-3y-2)*3^(3x-3-2y+5)=18
2^(4x-3y+2)*3^(3x-2y+2)=18
2^(4x-3y+2)*3^(3x-2y+2)=2*3^2
4x-3y+2=1
3x-2y+2=2
解得
x=2
y=2

x^y=2^3=8

Answer 3

[16^(x+1)*27^(x-1)]÷(2^(3y+2)*3^(2y-5)]=18
[(2^4)^(x+1)*(3^3)^(x-1)]÷[(2^(3y+2)*3^(2y-5)]=18
[2^(4x+4)*3^(3x-3)]÷[(2^(3y+2)*3^(2y-5)]=18
2^(4x+4-3y-2)*3^(3x-3-2y+5)=18
2^(4x-3y+2)*3^(3x-2y+2)=18
2^(4x-3y+2)*3^(3x-2y+2)=2*3^2
4x-3y+2=1
3x-2y+2=2
解得
x=2
y=3

x^y=2^3=8