1.将532写为根式,则正确的是()
A.352B.35
C.532D.53
解析:选D.532=53.
2.根式1a1a(式中a>0)的分数指数幂形式为()
A.a-43B.a43
C.a-34D.a34
解析:选C.1a1a=a-1??a-1?12=a-32=(a-32)12=a-34.
3.?a-b?2+5?a-b?5的值是()
A.0B.2(a-b)
C.0或2(a-b)D.a-b
解析:选C.当a-b≥0时,
原式=a-b+a-b=2(a-b);
当a-b0时,原式=b-a+a-b=0.
4.计算:(π)0+2-2×(214)12=________.
解析:(π)0+2-2×(214)12=1+122×(94)12=1+14×32=118.
答案:118
1.下列各式正确的是()
A.?-3?2=-3B.4a4=a
C.22=2D.a0=1
解析:选C.根据根式的性质可知C正确.
4a4=|a|,a0=1条件为a≠0,故A,B,D错.
2.若(x-5)0有意义,则x的取值范围是()
A.x5B.x=5
C.x5D.x≠5
解析:选D.∵(x-5)0有意义,
∴x-5≠0,即x≠5.
3.若xy≠0,那么等式4x2y3=-2xyy成立的条件是()
A.x0,y0B.x0,y0
C.x0,y0D.x0,y0
解析:选C.由y可知y0,又∵x2=|x|,
∴当x0时,x2=-x.
4.计算?2n+1?2??12?2n+14n?8-2(n∈N*)的结果为()
A.164B.22n+5
C.2n2-2n+6D.(12)2n-7
解析:选D.?2n+1?2??12?2n+14n?8-2=22n+2?2-2n-1?22?n??23?-2=2122n-6=27-2n=(12)2n-7.
5.化简23-610-43+22得()
A.3+2B.2+3
C.1+22D.1+23
解析:选A.原式=23-610-4?2+1?
=23-622-42+?2?2=23-6?2-2?
=9+62+2=3+2
6.设a12-a-12=m,则a2+1a=()
A.m2-2B.2-m2
C.m2+2D.m2
解析:选C.将a12-a-12=m平方得(a12-a-12)2=m2,即a-2+a-1=m2,所以a+a-1=m2+2,即a+1a=m2+2?a2+1a=m2+2.
7.根式a-a化成分数指数幂是________.
解析:∵-a≥0,∴a≤0,
∴a-a=-?-a?2?-a?=-?-a?3=-(-a)32.
答案:-(-a)32
8.化简11+62+11-62=________.
解析:11+62+11-62=?3+2?2+?3-2?2=3+2+(3-2)=6.
答案:6
9.化简(3+2)2010?(3-2)2011=________.
解析:(3+2)2010?(3-2)2011
=[(3+2)(3-2)]2010?(3-2)
=12010?(3-2)=3-2.
答案:3-2
10.化简求值:
(1)0.064-13-(-18)0+1634+0.2512;
(2)a-1+b-1?ab?-1(a,b≠0).
解:(1)原式=(0.43)-13-1+(24)34+(0.52)12
=0.4-1-1+8+12
=52+7+12=10.
(2)原式=1a+1b1ab=a+bab1ab=a+b.
11.已知x+y=12,xy=9,且xy,求x12-y12x12+y12的值.
解:x12-y12x12+y12=?x+y?-2?xy?12x-y.
∵x+y=12,xy=9,
则有(x-y)2=(x+y)2-4xy=108.
又xy,∴x-y=-108=-63,
代入原式可得结果为-33.
12.已知a2n=2+1,求a3n+a-3nan+a-n的值.
解:设an=t>0,则t2=2+1,a3n+a-3nan+a-n=t3+t-3t+t-1
=?t+t-1??t2-1+t-2?t+t-1=t2-1+t-2
=2+1-1+12+1=22-1.