(x-1/2)(2x+1)(2x^2+1/2)(4x^4+1/4)(16x^6+1/16)/(256x^16-1/256)

你中间有一项肯定是写错了，就是16x^6+1/16这一项，应该是16x^8+1/16，不然就没法做了。
观察(x-1/2)(2x+1)，对2x+1提取2，得：2(x+1/2)
所以：(x-1/2)(2x+1)=2(x-1/2)(x+1/2)=2(x²-1/4)=2x²-1/2
所以，原式=(2x²-1/2)(2x²+1/2)(4x^4+1/4)(16x^8+1/16)/(256x^16-1/256)
=(4x^4-1/4)(4x^4+1/4)(16x^8+1/16)/(256x^16-1/256)
=(16x^8-1/16)(16x^8+1/16)/(256x^16-1/256)
=(256x^16-1/256)/(256x^16-1/256)
=1
注：其实考察的就是平方差公式的运用。。。
祝你开心！希望能帮到你。。。

(x-1/2)(2x+1)(2x^2+1/2)(4x^4+1/4)(16x^6+1/16)/(256x^16-1/256)
=（2x^2-1/2）(2x^2+1/2)(4x^4+1/4)(16x^6+1/16)/(256x^16-1/256)
=(4x^4-1/4)(4x^4+1/4)(16x^6+1/16)/(256x^16-1/256)
=(16x^6-1/16)(16x^6+1/16)/(256x^16-1/256)
=(256x^16-1/256)/(256x^16-1/256)
=1

(x-1/2)(2x+1)(2x^2+1/2)(4x^4+1/4)(16x^6+1/16)/(256x^16-1/256)
=(2x^2-1/2)(2x^2+1/2)(4x^4+1/4)(16x^6+1/16)/(256x^16-1/256)
=(4x^4-1/4)(4x^4+1/4)(16x^6+1/16)/(256x^16-1/256)
=(16x^6-1/16)(16x^6+1/16)/(256x^16-1/256)
=(256x^16-1/256)/(256x^16-1/256)
=1

原式=(2x^2-1/2)(2x^2+1/2)×(4x^4+1/4)(16x^6+1/16)/(256x^16-1/256)
=(4x^4-1/4)(4x^4+1/4)(16x^6+1/16)/(256x^16-1/256)
=(16x^8-1/16)(16x^8+1/16)/(256x^16-1/256)
=(256x^16-1/256)/(256x^16-1/256)
=1