2024-2025學(xué)年新教材高中數(shù)學(xué)第四章指數(shù)函數(shù)對數(shù)函數(shù)與冪函數(shù)4.1.1實(shí)數(shù)指數(shù)冪及其運(yùn)算課時素養(yǎng)評價含解析新人教B版必修第二冊

PAGE實(shí)數(shù)指數(shù)冪及其運(yùn)算(15分鐘30分)1.QUOTE+QUOTE+(2019)0= ()A.6 B.7 C.8 D.QUOTE【解析】選B.QUOTE+QUOTE+QUOTE=2+4+1=7.2.(2024·遂寧高一檢測)下列各式計(jì)算正確的是 ()A.(-1)0=1 B.QUOTE·a2=a(a>0)C.QUOTE=8 D.a6÷a2=a3【解析】選A.(-1)0=1,A正確;QUOTE·a2=QUOTE,故B錯;QUOTE=QUOTE≠8,C錯;a6÷a2=a4,D錯.3.化簡QUOTE(其中a>0,b>0)的結(jié)果是 ()A.QUOTE B.-QUOTEC.QUOTE D.-QUOTE【解析】選C.QUOTE=QUOTE=QUOTE=QUOTE.4.若QUOTE=QUOTE,則實(shí)數(shù)a的取值范圍是 ()A.a∈R B.a=QUOTEC.a>QUOTE D.a≤QUOTE【解析】選D.左邊=QUOTE=QUOTE,所以|2a-1|=1-2a,即2a-1≤0.所以a≤QUOTE.【補(bǔ)償訓(xùn)練】QUOTE-(-2)0-QUOTE+QUOTE=________.

【解析】QUOTE-QUOTE-QUOTE+QUOTE=QUOTE-QUOTE-QUOTE+QUOTE=QUOTE-1-QUOTE+QUOTE=QUOTE.答案:QUOTE5.(2024·?？诟咭粰z測)計(jì)算下列各式(1)QUOTE;(2)2QUOTE÷QUOTE.【解析】(1)QUOTE=[-1×3×(-2)]QUOTE=6x0y1=6y;(2)2QUOTE÷QUOTE=[2×(-3)÷(-6)]QUOTE=x2y.(20分鐘40分)一、選擇題(每小題5分,共20分.多選題全部選對得5分,選對但不全的得3分,有選錯的得0分)1.計(jì)算:QUOTE= ()A.QUOTE+2 B.QUOTE-2C.-QUOTE-2 D.-QUOTE+2【解析】選C.原式=[(QUOTE-2)(QUOTE+2)]2019·(QUOTE+2)=(-1)2019·(QUOTE+2)=-QUOTE-2.【補(bǔ)償訓(xùn)練】已知fQUOTE=x+x-1-2,則f(x+1)= ()A.x2-4B.QUOTEC.QUOTE+(x+1)-2 D.x2+2x-3【解析】選D.因?yàn)閒QUOTE=QUOTE-4,所以fQUOTE=QUOTE-4=x2+2x-3.2.QUOTE的分?jǐn)?shù)指數(shù)冪表示為 ()A.QUOTE B.a3 C.QUOTE D.都不對【解析】選C.QUOTE=QUOTE=QUOTE=QUOTE=QUOTE.3.化簡QUOTE·QUOTE的結(jié)果是 ()A.-QUOTE B.QUOTEC.(a-1)4 D.QUOTE【解析】選B.因?yàn)镼UOTE·QUOTE,所以(a-1)3>0,即a-1>0,所以QUOTE·QUOTE=(a-1)·QUOTE=QUOTE=QUOTE.4.(多選題)在下列根式與分?jǐn)?shù)指數(shù)冪的互化中,不正確的是 ()A.(-x)0.5=-QUOTE(x≠0)B.QUOTE=QUOTEC.QUOTE=QUOTE(xy≠0)D.QUOTE=-QUOTE【解析】選ABD.對于A,若x<0,-QUOTE無意義,故A錯誤;對于B,當(dāng)y<0時,QUOTE≠Q(mào)UOTE,故B錯誤;對于C,由分?jǐn)?shù)指數(shù)冪可得xy>0,則QUOTE=QUOTE=QUOTE,故C正確;對于D,QUOTE=QUOTE=QUOTE,故D錯誤.所以不正確的是A,B,D.【補(bǔ)償訓(xùn)練】(多選題)下列各式運(yùn)算錯誤的是 ()A.(-a2b)2·(-ab2)3=-a7b8B.(-a2b3)3÷(-ab2)3=a3b3C.(-a3)2·(-b2)3=a6b6D.[-(a3)2·(-b2)3]3=-a18b18【解析】選C、D.對于A,(-a2b)2·(-ab2)3=a4b2·(-a3b6)=-a7b8,故A正確;對于B,(-a2b3)3÷(-ab2)3=-a6b9÷(-a3b6)=a6-3b9-6=a3b3,故B正確;對于C,(-a3)2·(-b2)3=a6·(-b6)=-a6b6,錯誤;對于D,[-(a3)2·(-b2)3]3=(a6b6)3=a18b18,錯誤.二、填空題(每小題5分,共10分)5.QUOTE+QUOTE-QUOTE+QUOTE=________.

【解析】QUOTE+QUOTE-QUOTE+QUOTE=QUOTE+2(-1)×(-2)-QUOTE+QUOTE=25+4-π+3-3=29-π答案:29-π6.(2024·北京師大附中高一檢測)化簡a2·QUOTE·QUOTE·QUOTE的結(jié)果是________.

【解析】a2·QUOTE·QUOTE·QUOTE=QUOTE=a2.答案:a2三、解答題7.(10分)化簡下列各式(1)QUOTE;(2)QUOTE.【解析】(1)原式=QUOTE·QUOTE=-2xy.(2)原式=QUOTE=QUOTE.【補(bǔ)償訓(xùn)練】1.解方程:(1)4x+2x+1-3=0;(2)22x+2+3×2x-1=0.【解析】(1)方程可化為QUOTE+2·2x-3=0.令t=2x(t>0),則t2+2t-3=0,解得t=1或t=-3(舍去).所以2x=1,解得x=0.(2)因?yàn)?2x+2+3×2x-1=0,所以4×QUOTE+3×2x-1=0.令t=2x(t>0),則方程可化為4t2+3t-1=0,解得t=QUOTE或t=-1(舍去),即2x=QUOTE,解得x=-2.2.(2024·重慶高一檢測)(1)計(jì)算:QUOTE+QUOTE-QUOTE+QUOTE;(2)設(shè)a>0,化簡:QUOTE;(3)若QUOTE+QUOTE=QUOTE,求QUOTE的值.【解析】(