若(x^m÷x^2×n)^3÷x^(m-n)与-1/4x^2为同类项,且2m+5n=7,求4m²-2n²旳值

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若(x^m÷x^2×n)^3÷x^(m-n)与-1/4x^2为同类项,且2m+5n=7,求4m²-2n²旳值若(x^m÷x^2×n)^3÷x^(m-n)与-1/4x^2为同类项,且

若(x^m÷x^2×n)^3÷x^(m-n)与-1/4x^2为同类项,且2m+5n=7,求4m²-2n²旳值
若(x^m÷x^2×n)^3÷x^(m-n)与-1/4x^2为同类项,且2m+5n=7,求4m²-2n²旳值

若(x^m÷x^2×n)^3÷x^(m-n)与-1/4x^2为同类项,且2m+5n=7,求4m²-2n²旳值
(x^m÷x^2×n)^3÷x^(m-n)
=(x^(m-2n))^3÷x^(m-n)
=x^3(m-2n)÷x^(m-n)
=x^(3m-6n-m+n)
=x^(2m-5n)
与-1/4x^2为同类项
所以
2m-5n=2
因为2m+5n=7
所以
4m=9
m=9/4
n=1/2
4m²-2n²
=4*(81/16)-2*(1/4)
=81/4 -1/2
=79/4