若3的m次方等于6,9的n次方等于2,则3的(2m-4n+1)次方等于?

问题描述:

若3的m次方等于6,9的n次方等于2,则3的(2m-4n+1)次方等于?

9=3的二次方,9的n次方就是3的2n次方,3的(2m-4n+1)将原式变形→
2(m-2n)+1
3 =(6*6/2*2)*3=27
不明白找我545925947

[说明:a^b表示a的b次方]
【解】
3^(2m-4n+1)
=[3^(2m)/3^(4n)]*(3^1)
=[(3^m)^2]/[9^(2n)]*3
=36/[(9^n)^2]*3
=36/4*3
=9*3
=27

=(3^m)^2×(3^n)^(-4)×3^1
=(3^m)^2×(9^n)^(-2)×3^1
=6^2×2^(-2)×3
=36×(1/4)×3
=27