高考数学《有理数的乘方》重难点试题-带解析

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⚪L13ᨵᳮᦟḄἠ♦⚪ூᦪ᱐௃஺஺ᱏூ1ᨵᳮᦪḄᭆ௃n!"ᦪḄ#Ḅ$%,'(,Ḅ)*'(ᗩ.ᓽᨵ.a1…1஺=4.ᙠ678஺'(9ᦪ8n'(ᢣᦪ.ூ⚪1ᨵᳮᦪḄᭆ௃2ூ<1௃=2020?•ᵞBCDEFG=HG3⊤KḄLMN=G2222A.=3GX=3Gx=3B.=3GX32x2x22C.3D.3x3x3ூT⚪UV௃᪷X⚪H7ḄYCZᨵᳮᦪḄLM8[\T]^⚪.2222ூT]_`௃T.IE*⊤KḄLMN=-§Gx=-5Gx=g,ᦑ⌱:4ூlYm1௃n3o3o3o3GᑏᡂḄrYN=G_
_4A.4.-s=-ᡈ.1Bu1⚓ᐳ14⚓

1ூT⚪UV௃᪷XxḄLMᓽ[yz]ᫀ8"!"ᦪ#Ḅ$%8'(.2ூT]_`௃T.-§}9ᦪḄ~᎛8⌕8ᦑ4⌱⚗┯29ᦪN5,ᦑ8⌱⚗┯ᙠᨬ☢ᨵ,ᦑ8⌱⚗┯2YᑏᡂḄrYN-=§G4,ᦑ஻⌱⚗ᦑ⌱:஻.ூlY1-2]=2020?•DE7Gᐵ=-5ḄḄN=GA.-5N9ᦪ,4NB.-5N9ᦪ,4Nᢣᦪ,625NC.-5N9ᦪ,4Nᢣᦪ8-625ND.5N9ᦪ,4NᢣᦪூT⚪UV௃ᑭᵨḄLMᑨᓽ[.ூT]_`௃T:ᐵ=-5ḄḄN-5N9ᦪ,4Nᢣᦪ,625Nx.ᦑ⌱.6.m22x2xx2ூlY1-3]=2020?•¡¢£E7G¤ᑏ3+3+……+3ḄN=G2m2m2mA.3nB.3nc.8D.3nூT⚪UV௃᪷XᨵᳮᦪḄT]ᓽ[.m2•----*----ஹom2X2X..X2ூT]_`௃T.3+3+:…+3rY©:ª,ᦑ⌱.4"3ூ2ᨵᳮᦪḄ$%௃=1GᦪḄ«¬ᗩ®Nᦪ=2GᦪḄ᜻uNᦪ,ᦪḄᏔᗩNᦪ=3G0Ḅ«¬᦮ᦪu®N0;=4GᨵᳮᦪḄ$%³ᨵᳮᦪḄ´◀$%᪵8✌ᐜ¹ºxḄ»,ᯠ½¾¿%xḄÀÁÂ.ூ⚪2ᨵᳮᦪḄ$%௃ூ<2௃=2020?•ÃÄ£EFGÅᑡᔜY)*ÈḄN=G232A.-22³=-2G28.[³=É32u2⚓ᐳ14⚓

2C.-=-2G³-I-21D.-12021³=-1G2021ூT⚪UV௃ᔜY¿%yᑮ)*8ᓽ[Ëzᑨ.ூT]_`௃T:/ஹ-22=-4,=-2G2=4,ÍÈ8Í»ᔠ⚪L;23_82_8^=3,=3G3=27,ÍÈ,Í»ᔠ⚪LC.-=-2G=2,-|-2|=-2,ÍÈ8Í»ᔠ⚪L;Dஹ-12021=-1,=-1G2021=7,È8»ᔠ⚪L.ᦑ⌱:D.ூlY2-1Ó=2020?•╋Õ£E7GÅᑡᔜÁᦪ78ᦪÂÈḄN=GA.-=-3G2³-=-2G3B.-32³=-3G2C.-3X23-^-32X2D.-23³=-2ூT⚪UV௃᪷XḄºMᑖ×T[y.ூT]_`௃T.4-=-3G2=-9,-=-2=8,ÍÈB.-32=-9,=-3=9,ÍÈC.-3X23=-24,-32X2=-18,ÍÈ;D.-23=-8,=-2G3=-8,Èᦑ⌱:஻ூlY2-2Ó=2020᧡•ÚÛD᪥ÝᨴὃGÅᑡ7ḄN=GA.Z=-aG஺ºNà©áᦪB.}஻©᜻ᦪ~8-a஻Z=-aG஻ÈC.}஻©Ꮤᦪ~8-âZ=-aG"ÈD.-ãZ=-aG”ºÍÈூT⚪UV௃᪷XᨵᳮᦪḄḄºM,ᑖ஻N᜻ᦪZᏔᦪåæçèéêTᓽ[.ூT]_`௃T.}஻©᜻ᦪ~8Z=-aG஻È8}஻©Ꮤᦪ~8-/Z=-aG”ºà©áᦪ.ᦑ⌱:ë=-lGn+=-lGn+2ூlY2-3Ó=2020?•íî£EFGï஻Nðᯠᦪ8ᑣ2Ḅ©=GA.1ᡈ-IB.0C.-1D.0ᡈ1ூT⚪UV௃ᑖ஻©᜻ᦪZᏔᦪåæçè,᪷Xᨵᳮᦪ$%ᑣ¿%[y.u3⚓ᐳ14⚓

3(-l)n+(-l)n+2_-1-1_[T]_`௃T:ó஻©᜻ᦪ,ᑣ2ôN᜻ᦪ,õ~2=21(-l)n+(-l)n+2_l+l_ón©Ꮤᦪ,ᑣ2ô©Ꮤᦪ8õ~211ᦑ⌱:4ூ3ᏔḄöឋ௃«¬ᦪḄᏔu®Nöᦪ,ᓽa?>0.ூ⚪3ᏔḄöឋ௃ூ<3௃(2021᧡•ùúûDE7)ý(2x-4)2+|ᡝ2-81=0,ᑣ(*-8)2஺21=.ூT⚪UV௃ᵫ
ᦪḄᐭஹyḄᐭᓽ.ூ௃(2x-4)2+|ᡝ28|=0,.".2A--4=0,ᡝ28=0,x—2,y=3,a-y)2021=(2-3)2021=(7)2*-1,ᦑᫀ"-1.ூ$%3-1](2020&•()*᪥,-.)0aஹ8"᦮ᦪ2|a-21+33320=1,ᑣ஻=.ூ⚪89௃ᐜᑭᵨ=>?@AḄᑮa=lᡈ3,3=-3ᡈa=2,6=-4ᡈ-2,ᯠEᑭᵨḄFG.ூ௃:•••I_2„3)2020K0,Laஹ6"᦮ᦪ/.Ia-21=1,(/H-3)2020=0ᡈIa-2I=0,(N3)2020=1,a—lᡈ3,8=-3ᡈa=2,b=-4ᡈ-2,Oa=l,6=-3P,tf=-3;Oa=3,6=-3P,஻=(-3>=-27;Oa=2,b=-4,kP=(-4)2=16;Oa=2,6=-2PbP=(-2*=4;RSᡠU,஻=(-3=-27;Ḅ"-3ᡈ-27ᡈ4ᡈ16.ᦑᫀ"-3ᡈ-27ᡈ4ᡈ16.ூ$%3-2](2020&•⊝W-.)>X|a-11-3Y-(ᵪ3/+2,[[?\\]^_`ab[[Ḅab|a-1-3ᨵᨬe,ᨬe"3f4⚓ᐳ14⚓

4\\Ḅab-iᓡ3l2+2ᨵᨬᜧ,ᨬᜧ"2>XISabᑣilA.[[?\\ᙳrsB.[[rs,\\ursC.[[urs\\rsD.[[?\\ᙳursூ⚪89௃᪷yᨵᳮᦪḄ{Aஹ=>Ḅ|ᓽ.ூ௃:}"la-1|0,ᡠI|a-1|-3ᨵᨬeᨬe"-3;}"i63l22஺ᡠI-iN3l2W0,ᡠI-i3l2+2ᨵᨬᜧ,ᨬᜧ"2,ᡠI[[urs\\rsᦑ⌱:C.ூ$%3-3]i2020&•-.l0aஹ஺ᨵᳮᦪᑡᑨজ+i91l2rᦪ;ঝ/+஻+1rᦪঞ9+ia--Ḅᨬe"9ট1-QN1l2Ḅᨬᜧ0ᐸ.┯Ḅ`ᦪilA.IB.2C.3D.4[⚪89௃¡¢ᑭᵨᏔAḄឋ¥ᑖ§ᑖ᪆ᫀ.i[:জ+iN1l2
ᦪ,ᦑ©⌱┯ঝ/+/+1rᦪ,rsঞ9+ia-6l2Ḅᨬe"9,rsট1-iaª1"Ḅᨬᜧ1,ᦑ©⌱⚗┯.ᦑ⌱:8.ூ®¯b4°@AḄ±ᔠ³௃ᨵᳮᦪ±ᔠ³Ḅ´µ:i1lᐜ@A,@◀,ᨬEN·i2l¸,³,ª¹ᑮºFGi3l᝞ᨵ¼½,ᐜ¾¼½ᑁḄ³ᢥe¼½ஹ.¼½ஹᜧ¼½ÁFG.ூ⚪Â4°@AḄ±ᔠ³௃21—3?+[4—i—1l2]+[—i—l2]x24ூÆ4௃i2021᧡•ÈÉ*-Êl3J.ூ⚪89௃ᑭᵨᨵᳮᦪ±ᔠ³ḄÌᑣ³:ᐜ¾@A¾@◀,ᨬE¾N·,ᨵ¼½Ḅᐜ¾¼½Íf5⚓ᐳ14⚓

5☢Ḅ.21ூ௃:Ð%=-9^(4-1)+(3-4)X2421Óx—x=-94-3+(324424)=-3+(16-6)=-3+10=7.1x——ூ$%4-1](2020&•ÕÖ-Ê)[2+(-5)2]+33|-|+23.4ூ⚪89௃ᐜ@A,@◀,ᨬEN·.¸,³,ª¹×º.1X--ூ௃:Ð%=[2+25]+334+81X--=274-334+81xÓÓ=934+8=3-4+8=7.-I2012-[2-(-3)2]-(1-+2--3.75)X24ூ$%4-2](2021᧡•᜽Ù*-.)83.ூ⚪89௃ᐜ@A,@Ì,ᨬEN·;¸,³,Úᢥª¹ᑮºḄ´µFG;᝞Ûᨵ¼½,⌕ᐜ¾¼½ᑁḄ³.Ý@ÌᑖÞßḄᮣá³ᵨ.31-12012_[2-(-3)2]-(1-+2__3.75)x24ூ௃8311715---X--Xd----X=-1-(2-9)824324424=-1+7-33-56+90/_])2021+12+|-è|x(-4)Ó(Ó2?)x(-ூ$%4-3](2021᧡•ãäå*ᨴὃ):1Óqூ⚪89௃᪷yᨵᳮᦪḄ@AஹᨵᳮᦪḄ@◀Ì?N·ÌIê⚪.(-1)2021+12^|-^|X(-4)-(-22)X(-ூ௃45X-X=(-1)+123(-4)-(-4)x(=(-1)-64-56f6⚓ᐳ14⚓

6=-70.ூ⚪Â5@AḄÚᵨëß௃22ìÆ5íi2020&•ᓲï-ÊlÓ᪷1NðḄñò,fÓóôñòḄõföóôᒕñòḄø᝞©óô,f100óùEᒕñòḄðúilAeûüm2ூ⚪89௃᪷yᨵᳮᦪḄ@AḄ|ᓽ.21ூ௃fÓóôñòḄᵨýᒕ§N21212föóôᒕñòḄýᒕ51=ÿᐁ21.••100ᒕḄ§,ᒕḄG1°°ᦑ⌱:C.ூ5-1#$2021᧡•&ᓅ()*+,-.ᙠ01234,5678ᑖ:1,5;ᑖ<=>?,-.ᵫ;Aᑖ:ᑮ16A,DE?A23⌕G2ᑖH.ூI⚪KL௃᪷O-.ᙠ01234,5678ᑖ:1,ᑣn78,ᑖ:ᑮ22஻A,RSᑡU3VI.ூIW23௃I:XG2஻78=᪷O⚪Y=Z22஻=16,2/3=4,77-2.278=120ᑖH=ᦑWᫀa120.ூ5-2#b2cdeḄfghi⍝:klmnᑖop,q᤯o;sᡂ2Alm;?vAlm᤯o;,ᐳᡂ4Alm;?4Almx,yᡂ8Alm…ᎷXlm;}~30,DEnᨵAklmூI⚪KL௃᪷OᨵᳮᦪUḄ,ᓄ30,klmḄAᦪ2X2X...X2$30A2=23°$A.7⚓ᐳ14⚓

7ூIW23௃I:ᓄ;,klmḄAᦪ2=21$Aᓄv,klmḄAᦪ2X2=22=4$A;ᓄ,klmḄAᦪ2X2X2=23=8$Aᓄ=klmḄAᦪ2X2X2X2=24=16$A,ᓄ30,klmḄAᦪ2X2X...X2$30A2=23஺$A.,lm;}~30,nᨵ23஺Aklm.ூ5-3]$2020•)4ᨵ;,Ḅ0.1,>v¡¢ᙠ;£=¤¥¦ᢚ;,22X0.1.$1¦ᢚ2,$2¦ᢚ6=ூI⚪KL௃$1᪷O¦ᢚ¨©ªᡠVᓽ$2᪷O¦ᢚ¨©ªᡠVᓽ.ூIW23௃Ia$1᪷O⚪YZ:2X22X0.1=0.8$$2᪷O⚪YZ:25*22®0.1=12.8$.ூ⚪¯6U°ᵨ4Ḅ²³⚪௃[µ6]$2021•¶·:>10¸ᑣx=logioNx¿10ÀḄ4Ḅ¦ᦪ,ÁeIgN,ᐸÃÄÅÆÇᑣa/ÈÉ$ÊË$M>0,Ë>0.µ᝞:Ï102=100,ᡠ2=/gl00,Ðᓽ75-100-2;7^4+7^3=7^12.᪷OÓÔÕÅÆÇᑣ=ÖÆ$Ë22+•Ë5+/ᡂḄ×Ø$A.5B.2C.1D.0ூI⚪KL௃᪷O⚪Y=ᢥ᯿⚪ßḄÅÆÇᑣÖÆᓽ.ூIW23௃Ia$/Ḅ2+/ᡈ•=á+஻5=/⊟$/ã+/ಘ+/å=11=lgio=1.ᦑ⌱:ூ6-1]$2020•æç(᪥é)4êëì▅î☢ᩞᧇ=òIWᑡ³⚪.᝞Øaa>0,a/lḄ6ᗩõöAᓽᢣᦪab=N,DEᦪbøùaÀúḄ¦ᦪ,¦ᦪeûa88⚓ᐳ14⚓

8loga/V=6.µ᝞aজÏᢣᦪ22=4,ᡠ2À4Ḅ¦ᦪþ2,¦ᦪeûaIog24=2;ঝᢣᦪ42=16,ᡠ416Ḅᦪ2,ᦪlog416=2.(1)᪷☢▅#ᩞᧇ&'ᑡᢣᦪᦋᦪজ62=36;ঝ43=64;(2)&'ᑡᦪᦋᢣᦪজlog525=2;@log27=3;3ব01log232.ூ3⚪56௃(1)᪷ᦪḄ89:3;(2)ᑭᵨᦪḄ89ᑏᡂ@ḄA;(3)ᐜᑭᵨCDḄE9Fᑮ25=32,ᯠI᪷ᦪḄ89:3.ூ3JKL௃3:পজ62=36;ᦪlog636=2;ঝ43=64;ᦪIog/164=3;ফজIog525=2;ᢣᦪ52=25,@log27=3;3ᢣᦪ33=27;(3)=25=32,log32=5.2ூR6-2](2020V•XᓄZᨴὃ)(1)01'☢]^1জ(3X5)2`32X52;ঝ[(-2)X3]2`(-2)2X32;(2)᪷01bcde(f)3ghijk(lmᑏnbc)(3)de`opq஻s᦮ᦪuvghijkwᑭᵨCDḄE9xyᳮᵫ.ভᑭᵨ}b~v:(-4)2020x0.25202௃Ḅ.9⚓ᐳ14⚓

9ூ3⚪56௃(1)᪷⚪E01nbcᓽ(2)᪷(1)Ḅ01bcᑏndeᓽ.(3)q"s᦮ᦪu,ᑏndeḄbc,ᯠI᪷CDḄE9xyᳮᵫᓽ.(4)ᑭᵨ(3)Ḅb~01nᓽ.ூ3JKL௃3(1)01'☢]^1জ(3X5)2=225;32X52=9X25=225.ঝ[(-2)X3]2=36;(-2)2X32=4X9=36.(2)᪷(1)01bcdeঢᔖ஻.(3)q஻s᦮ᦪuv(a6)஻=/.ᳮᵫq஻s᦮ᦪu.=ab-ab…ab-ab=a-Q…Q•ab-b…bb=00(ab)”nḄCnaḄ•nbḄanbn.ᓽq"s᦮ᦪuv(4஺)"=.(4)(-4)2020X0.252021=(-4)2020X0.252020X0.25=(-4X0.25)2020XO.25=0.25.ூR6-3](2020V•)ᭆ8::¡¢Ḅᨵᳮᦪ(ᙳ¥gh0)Ḅ◀§¨1©ª◀D,᝞2+2+2,(-3)+(-3)+(-3)+(-3)g,¬ᨵᳮᦪḄCD,ᡃ¯°22+22ঞ,#“2Ḅᙌ3³D“v(-3)+(-3)+(-3)+(-3)(-3)®,#“-3Ḅᙌ4³D”v¶·ᙢ,°஻a(aWO)Q+Q+Q+............+CLna,a¹#“aḄᙌ஻³D”.º»¼½:lmᑏn01bc2ঞ=,(-5)°=;¾ᐭ5ὃ1111177À᝞(-3)®=(-3)+(-3)+(-3)+(-3)=(¶ᑓ"(-§)*(-§)x(-§)=(-§)=(§)(1)ĶÄ:Å᯿☢Ḅ1v&'ᑡ¨1bclmᑏᡂᗩḄA.5®=;(-2)O=;2z+(È)টx(-2)ঞ-()v-஺ফ1¶1I3v3,ঠ+33.ூ3⚪56௃(1)ᑭᵨË89:3;(2)ᐜ°◀D¨1ÌᓄCD¨1ÍÎ01,ᯠIÍÎC◀¨1.ூ3JKL௃32ঞ=5(-3ঞ=¶2;(1)5ড=('(¶/ড=2ஹ1010⚓ᐳ14⚓

1022+(È)টX(_2)ঞ_(È)vஹ°(2)V3J®4-33=22+(-x(-2)1-(-37+27211=4x—x(--)+27+2792_7-9.18ZᦑJᫀ2;-2;(1)5^;2%ফ9.ூßàá5âᦪ§Ḅ⊤ä௃(1)âᦪ§:°¶ᜧh10ḄᦪᡂaX10nḄA,ᐸa᦮ᦪᦪéêᨵ¶éḄᦪ,ns᦮ᦪ,ëìᦪ§©ªâᦪ§.ூâᦪ§A:aXIOn,ᐸiWa<10,ns᦮ᦪ.௃(2)ñD§òbজâᦪ§aḄ⌕:ô10ḄᢣᦪnḄ⊤äñᐵövᵫh10Ḅᢣᦪ÷ᩭḄ᦮ᦪéᦪù1;ᢥûñ,ᐜᦪ¶'÷ᦪḄ᦮ᦪéᦪ,ᓽ:n10Ḅᢣᦪn.ঝᦪ§⌕:ᜧh10Ḅᦪᵨâᦪ§⊤ä,üýþᜧh10Ḅÿᦪ
᪵ᵨ⊤,☢.ூ⚪7ᦪḄ⊤௃[7](2021᧡•'()*+,)᝞/0123452009789Ḅ:☢;<100=>Ḅ1ᐗ0@A:100=>1ᐗBCDE1FᐗḄG;,ᙠIᙢ0:A᪵ḄKἠMN⚔PQ☢ᒹ.“100=>”Uᵨᦪ⊤()■MnmonA.1X1O1OB.1X1O12C.1X1O13D.1X1014ூ^⚪_`௃ᦪḄ⊤ab=100X104X108=100000000000000=1X1014.11⚓ᐳ14⚓

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