Ответы к странице 220
874. Представьте выражение в виде степени с основанием a или произведения степеней с разными основаниями:
1) a−7∗a10;
2) a−9∗a5;
3) a17∗a−4∗a−11;
4) a−2:a3;
5) a12:a−4;
6) a−7:a−11;
7) a−12:a−10∗a4;
8) (a3)−5;
9) (a−12)−2;
10) (a−3)4:(a−2)5:(a−1)−7;
11) (m−3n4p7)−4;
12) (a−1b−2)−3;
13) (x3y−4)5∗(x−2y−3)3;
14) (a11b−7c−3d4)−3;
15) (a−7b5)−3∗(a4b−7)−5.
Решение:
1) a−7∗a10=a−7+10=a3
2) a−9∗a5=a−9+5=a−4
3) a17∗a−4∗a−11=a17−4−11=a2
4) a−2:a3=a−2−3=a−5
5) a12:a−4=a12−(−4)=a12+4=a16
6) a−7:a−11=a−7−(−11)=a−7+11=a4
7) a−12:a−10∗a4=a−12−(−10)+4=a−12+10+4=a2
8) (a3)−5=a3∗(−5)=a−15
9) (a−12)−2=a−12∗(−2)=a24
10) (a−3)4:(a−2)5:(a−1)−7=a−3∗4:a−2∗5:a−1∗(−7)=a−12:a−10:a7=a−12−(−10)−7=a−12+10−7=a−9
11) (m−3n4p7)−4=m−3∗(−4)n4∗(−4)p7∗(−4)=m12n−16p−28
12) (a−1b−2)−3=a−1∗(−3)b−2∗(−3)=a3b6
13) (x3y−4)5∗(x−2y−3)3=x3∗5y−4∗5∗x−2∗3y−3∗3=x15y−20∗x−6y−9=x15−6y−20−9=x9y−29
14) (a11b−7c−3d4)−3=a11∗(−3)b−7∗(−3)c−3∗(−3)d4∗(−3)=a−33b21c9d−12=a−33b21c−9d12
15) (a−7b5)−3∗(a4b−7)−5=a−7∗(−3)b5∗(−3)∗a4∗(−5)b−7∗(−5)=a21b−15∗a−20b35=a21−20b−15+35=ab20=ab−20
875. Найдите значение выражения:
1) 11−23∗1125;
2) 317∗3−14;
3) 4−16:4−12;
4) 10−15:10−14∗10−2;
5) (14−10)5∗(14−6)−8;
6) 3−12∗(3−6)−3(3−3)−4∗(3−4)2.
Решение:
1) 11−23∗1125=11−23+25=112=121
2) 317∗3−14=317−14=33=27
3) 4−16:4−12=4−16−(−12)=4−16+12=4−4=144=1256
4) 10−15:10−14∗10−2=10−15−(−14)−2=10−15+14−2=10−3=1103=11000
5) (14−10)5∗(14−6)−8=14−10∗5∗14−6∗(−8)=14−50∗1448=14−50+48=14−2=1142=1196
6) 3−12∗(3−6)−3(3−3)−4∗(3−4)2=3−12∗3−6∗(−3)3−3∗(−4)∗3−4∗2=3−12∗318312∗3−8=3−12+18312−8=3634=36−4=32=9
876. Найдите значение выражения:
1) 25−3∗58;
2) 64−3:32−3;
3) 10−10:1000−3∗(0,001)−5;
4) (−27)−12∗9581−4∗3−7;
5) 154∗5−645−3∗39;
6) (0,125)−8∗16−732−2.
Решение:
1) 25−3∗58=(52)−3∗58=5−6∗58=52=25
2) 64−3:32−3=(26)−3:(25)−3=2−18:2−15=2−3=123=18
3) 10−10:1000−3∗(0,001)−5=10−10:(103)−3∗(10−3)−5=10−10:10−9∗1015=10−10+9+15=1014=100000000000000
4) (−27)−12∗9581−4∗3−7=((−3)3)−12∗(32)5(34)−4∗3−7=(−3)−36∗3103−16∗3−7=3−263−23=3−3=133=127
5) 154∗5−645−3∗39=(3∗5)4∗5−6(9∗5)−3∗39=34∗54∗5−6(32∗5)−3∗39=34∗5−2(32)−3∗5−3∗39=34∗5−23−6∗5−3∗39=34∗5−25−3∗33=34−3∗5−2+3=3∗5=15
6) (0,125)−8∗16−732−2=((0,5)3)−8∗(24)−7(25)−2=(12)−24∗2−282−10=224−28+10=26=64
877. Упростите выражение:
1) 35x−3y5∗59x4y−7;
2) 0,2a12b−9∗50a−10b10;
3) −0,3a10b7∗5a−8b−6;
4) 0,36a−5b6c3∗(−229)a4b−4c−5;
5) 2x7∗(−3x−2y3)3;
6) (a2b9)−3∗(−2a4b10);
7) (−5a−3b2c−2)−2∗(0,1a2b−3c)−3;
8) 0,1m−5n4∗(0,01m−3n)−2;
9) −614a−7b4∗(52a−2b2)−3;
10) −(4a−4b3)−2∗(−18a3b−3)−3;
11) 19a−1533b−14∗11b−1176a−17;
12) (9x−35y−2)−2∗(27x−2y4)2.
Решение:
1) 35x−3y5∗59x4y−7=35∗59x−3+4y5−7=13xy−2
2) 0,2a12b−9∗50a−10b10=0,2∗50a12−10b−9+10=10a2b
3) −0,3a10b7∗5a−8b−6=−0,3∗5a10−8b7−6=−1,5a2b
4) 0,36a−5b6c3∗(−229)a4b−4c−5=36100∗(−209)a−5+4b6−4c3−5=925∗(−209)a−1b2c−2=−45a−1b2c−2
5) 2x7∗(−3x−2y3)3=2x7∗(−27x−6y9)=−54xy9
6) (a2b9)−3∗(−2a4b10)=a−6b−27∗(−2a4b10)=−2a−2b−17
7) (−5a−3b2c−2)−2∗(0,1a2b−3c)−3=125a6b−4c4∗1000a−6b9c−3=40b5c
8) 0,1m−5n4∗(0,01m−3n)−2=0,1m−5n4∗10000m6n−2=1000mn2
9) −614a−7b4∗(52a−2b2)−3=−254a−7b4∗(52)−3a6b−6=−(52)2a−7b4∗(52)−3a6b−6=−(52)−1a−1b−2=−25a−1b−2
10) −(4a−4b3)−2∗(−18a3b−3)−3=−((22)a−4b3)−2∗(−(2−3)a3b−3)−3=−2−4a8b−6∗(−29a−9b9)=25a−1b3=32a−1b3
11) 19a−1533b−14∗11b−1176a−17=a−153b−14∗b−114a−17=a−15b−1112a−17b−14=12a−15+17b−11+14=12a2b3
12) (9x−35y−2)−2∗(27x−2y4)2=(5y−29x−3)2∗((33)x−2y4)2=(5y−232x−3)2∗36x−4y8=25y−434x−6∗36x−4y8=25∗36−4x−4+6y−4+8=25∗32x2y4=25∗9x2y4=225x2y4
878. Упростите выражение:
1) (a−5−1)(a−5+1)−(a−5−2)2;
2) y−2−x−2x+y;
3) a−3−3b−6a−6−2a−3b−6+b−12−a−3+3b−6a−6−b−12;
4) m−4+n−4n−10:m−4n−6+n−10n−2;
5) x−2x−2−y−2:(x−2x−2−y−2−x−2+y−2x−2);
6) x−10−4x−5∗1x−5+2−x−5+2x−5;
7) (4c−6c−6+1−c−6c−12+2c−6+1):4c−6+3c−12−1+2c−6c−6+1.
Решение:
1) (a−5−1)(a−5+1)−(a−5−2)2=(a−5)2−1−((a−5)2−4a−5+4)=a−10−1−(a−10−4a−5+4)=a−10−1−a−10+4a−5−4=4a−5−5
2) y−2−x−2x+y=1y2−1x2x+y=x2−y2x2y2x+y=x2−y2x2y2∗1x+y=(x−y)(x+y)x2y2∗1x+y=x−yx2y2
3) a−3−3b−6a−6−2a−3b−6+b−12−a−3+3b−6a−6−b−12=a−3−3b−6(a−3−b−6)2−a−3+3b−6(a−3−b−6)(a−3+b−6)=(a−3−3b−6)(a−3+b−6)−(a−3−b−6)(a−3+3b−6)(a−3−b−6)2(a−3+b−6)=a−6−3a−3b−6+a−3b−6−3b−12−(a−6−a−3b−6+3a−3b−6−3b−12)(a−3−b−6)2(a−3+b−6)=a−6−3a−3b−6+a−3b−6−3b−12−a−6+a−3b−6−3a−3b−6+3b−12(a−3−b−6)2(a−3+b−6)=−4a−3b−6(a−3−b−6)2(a−3+b−6)
4) m−4+n−4n−10:m−4n−6+n−10n−2=m−4+n−4n−10∗n−2m−4n−6+n−10=m−4+n−4n−10∗n−2n−6(m−4+n−4)=1n−10∗n−2n−6=n10−2+6=n14
5) x−2x−2−y−2:(x−2x−2−y−2−x−2+y−2x−2)=x−2x−2−y−2:x−4−(x−2−y−2)(x−2+y−2)x−2(x−2−y−2)=x−2x−2−y−2:x−4−(x−4−y−4)x−2(x−2−y−2)=x−2x−2−y−2:x−4−x−4+y−4x−2(x−2−y−2)=x−2x−2−y−2∗x−2(x−2−y−2)y−4=x−21∗x−2y−4=x−4y−4=y4x4=(yx)4
6) x−10−4x−5∗1x−5+2−x−5+2x−5=(x−5−2)(x−5+2)x−5∗1x−5+2−x−5+2x−5=x−5−2x−5−x−5+2x−5=x−5−2−(x−5+2)x−5=x−5−2−x−5−2x−5=−4x−5=−4x5
7) (4c−6c−6+1−c−6c−12+2c−6+1):4c−6+3c−12−1+2c−6c−6+1=(4c−6c−6+1−c−6(c−6+1)2)∗c−12−14c−6+3+2c−6c−6+1=4c−6(c−6+1)−c−6(c−6+1)2∗(c−6−1)(c−6+1)4c−6+3+2c−6c−6+1=4c−12+4c−6−c−6c−6+1∗c−6−14c−6+3+2c−6c−6+1=4c−12+3c−6c−6+1∗c−6−14c−6+3+2c−6c−6+1=c−6(4c−6+3)c−6+1∗c−6−14c−6+3+2c−6c−6+1=c−6c−6+1∗c−6−11+2c−6c−6+1=c−6(c−6−1)+2c−6c−6+1=c−12−c−6+2c−6c−6+1=c−12+c−6c−6+1=c−6(c−6+1)c−6+1=c−6=1c6
