作业帮1.计算3/2(1+1/2^2)(1+1/2^4)...(1+1/2^64)(1+1/2^128)+2^(-255)2.(81^2m)/(9^2m)/(3^m)=81,求m3.先化简,再求值.{[(a^2-b^2)/ab]^2}/{(a+b)[(a-b)/a]^3}/(a/b^2),其中a/b=2/3.
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1.计算3/2(1+1/2^2)(1+1/2^4)...(1+1/2^64)(1+1/2^128)+2^(-255)2.(81^2m)/(9^2m)/(3^m)=81,求m3.先化简,再求值.{[(a^2-b^2)/ab]^2}/{(a+b)[(a-b)/a]^3}/(a/b^2),其中a/b=2/3.
1.计算3/2(1+1/2^2)(1+1/2^4)...(1+1/2^64)(1+1/2^128)+2^(-255)
2.(81^2m)/(9^2m)/(3^m)=81,求m
3.先化简,再求值.{[(a^2-b^2)/ab]^2}/{(a+b)[(a-b)/a]^3}/(a/b^2),其中a/b=2/3.
1.计算3/2(1+1/2^2)(1+1/2^4)...(1+1/2^64)(1+1/2^128)+2^(-255)2.(81^2m)/(9^2m)/(3^m)=81,求m3.先化简,再求值.{[(a^2-b^2)/ab]^2}/{(a+b)[(a-b)/a]^3}/(a/b^2),其中a/b=2/3.
1 3/2(1+1/2^2)(1+1/2^4)...(1+1/2^64)(1+1/2^128)+2^(-255)
=2(1-1/2^2)(1+1/2^4).(1+1/2^128)+2^(-255)
=2(1-1/2^4).(1+1/2^128)+2^(-255)
=2(1-1/2^256)+2^(-255)
=2-1/2^255+1/2^255
=2
2 .(81^2m)/(9^2m)/(3^m)=3^(6m)*3(-4m)*3^(-m)=3^(6m-4m-m)=3^(m)=81=3^4
则m=4
3 .{[(a^2-b^2)/ab]^2}/{(a+b)[(a-b)/a]^3}/(a/b^2)
=[(a^2-b^2)^2/(ab)^2]/[(a^2-b^2)(a-b)^2/a^3]/(a/b^2)
=a(a-b)(a+b)/[(a-b)^2*b^2]/(a/b^2)
=(a+b)/(a-b)
=(a/b+1)/(a/b-1)
代入a/b=2/3
原式=(2/3+1)/(2/3-1)=-5
东方神不散的，。不541353546845456454555555555555555555555555555555143545645456
81^(2m)=9^(4m)=3^(8m)
9^(2m)=3^(4m)
所以 原式=3^(8m)/3^(4m)/(3^m)=3^(3m)
1 3/2(1+1/2^2)(1+1/2^4)...(1+1/2^64)(1+1/2^128)+2^(-255)
=2(1-1/2^2)(1+1/2^4).....(1+1/2^128)+2^(-255)
=2(1-1/2^4)....(1+1/2^128)+2^(-255)
=2(1-1/2^256)+2^(-255)
=2-1/2^255+1/2^255
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1 3/2(1+1/2^2)(1+1/2^4)...(1+1/2^64)(1+1/2^128)+2^(-255)
=2(1-1/2^2)(1+1/2^4).....(1+1/2^128)+2^(-255)
=2(1-1/2^4)....(1+1/2^128)+2^(-255)
=2(1-1/2^256)+2^(-255)
=2-1/2^255+1/2^255
=2
2 .(81^2m)/(9^2m)/(3^m)=3^(6m)*3(-4m)*3^(-m)=3^(6m-4m-m)=3^(m)=81=3^4
则m=4
3 .{[(a^2-b^2)/ab]^2}/{(a+b)[(a-b)/a]^3}/(a/b^2)
=[(a^2-b^2)^2/(ab)^2]/[(a^2-b^2)(a-b)^2/a^3]/(a/b^2)
=a(a-b)(a+b)/[(a-b)^2*b^2]/(a/b^2)
=(a+b)/(a-b)
=(a/b+1)/(a/b-1)
代入a/b=2/3
原式=(2/3+1)/(2/3-1)=-5 (知道了吗？）
收起
3/2(1+1/2^2)(1+1/2^4)...(1+1/2^64)(1+1/2^128)+2^(-255)
=2(1-1/2^2)(1+1/2^2).....(1+1/2^128)+2^(-255)
=2(1-1/2^4)(1+1/2^4)....(1+1/2^128)+2^(-255)
=2(1-1/2^256)+2^(-255)
=2-1/2^255+1/2^...
全部展开
3/2(1+1/2^2)(1+1/2^4)...(1+1/2^64)(1+1/2^128)+2^(-255)
=2(1-1/2^2)(1+1/2^2).....(1+1/2^128)+2^(-255)
=2(1-1/2^4)(1+1/2^4)....(1+1/2^128)+2^(-255)
=2(1-1/2^256)+2^(-255)
=2-1/2^255+1/2^255
=2
2 .(81^2m)/(9^2m)/(3^m)=3^(6m)*3(-4m)*3^(-m)=3^(6m-4m-m)=3^(m)=81=3^4
则m=4
3 .{[(a^2-b^2)/ab]^2}/{(a+b)[(a-b)/a]^3}/(a/b^2)
=[(a^2-b^2)^2/(ab)^2]/[(a^2-b^2)(a-b)^2/a^3]/(a/b^2)
=a(a-b)(a+b)/[(a-b)^2*b^2]/(a/b^2)
=(a+b)/(a-b)
=(a/b+1)/(a/b-1)
代入a/b=2/3
原式=(2/3+1)/(2/3-1)=-5
收起